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geometry2

geometry2Since A'C' is parallel to AC, then the triangles BA'C' and BAC are similar. We'll use the proportionality of the lengths of the sides to determine the unknowns: A'C'/AC = BA'/BA = BC'/BC Let BC' =...

geometry2To evaluate the area of the triangle ABC, we must find out first the x and y intercepts of the graph of the function f(x) = 2x + 5. To calculate x intercept, we'll have to cancel y = 0. But y =...

geometry2Let d = diagonal, l = length, w = widthSince we know that the diagonal of the rectangle splits the rectangle into two right angle triangles, being the hypotenuse of both right angle triangles.To...

geometry2We must solve the system formed by the equations of the given lines to verify if it has any solutions. (x1)/2  y=5 We'll multiply by 2: x  1  2y = 10 We'll add 1: x  2y = 11 (1) x + (1y)/4=6...

geometry2To calculate the sum a +3b + 5c, we'll have to calculate first the vectors 3b and 5c: 3b = 3(2i  3j) 5c = 5( i +j) Computing the sum of 3 vectors, yields: a +3b + 5c = a + 3(2i  3j) + 5( i +j)...

geometry2Since the given points lie on the graph of f(x), their coordinates verify the expression of f(x). f(1) = 3 and f(3) =7 We'll put x = 1 in the expression of condition from enunciation: a*f(1+2) +...

geometry2DistanceThe abscisa and the ordinate of a point in the cartesian plane is (3, 4).Find the distance.We'll get the abscisa and the ordinate of a point, tracing perpendiculars from the given point to x and y axis. We'll form a right angle triangle, whose hypotenuse is the distance from origin to...

geometry2First, we'll write the equation of the line that passes AB. (xB  xA)/(xxA) = (yByA)/(yyA) We'll substitute the coordinates for A and B: (b3)/(x3) = (42)/(y2) (b3)/(x3) = 6/(y2) We'll...

geometry2We'll write the perimeter of the triangle as the sum of the lengths of the sides: x + y + 10 = 24 (1) Since it is a right angle triangle, we'll use the Pythagorean theorem to calculate the...

geometry2Verify if the point is a solution for the systemVerify if the point (1,3) is a solution for the...To verify if the pair (1,3) is the solution of the system, we have to substitute x and y by the values 1 and 3 to check if they cancel the equations. We'll substitute (1,3) in the first...

geometry2For the given quadrilateral ABCD: Length of AB = sqrt(8^2 + 1^2) = sqrt 65, slope of AB = (1/8) Length of BC = sqrt(4^2 + 7^2) = sqrt 65, slope of BC = 7/4 Length of CD = sqrt(8^2 + 1^2) = sqrt...

geometry2Rectangles.The perimeter of a rectangle is 7 times its width. What are its sides if the area is 40 ?Let the length and width of the rectangle be L and W. The perimeter of a rectangle is 7 times its width. => 2L + 2W = 7W => 2L = 5W => L = (5/2)W Area = 40 => L*W = 40 => (5/2)W*W =...

geometry2It is given that the circle is tangent to the y axis and has a radius of three units. This implies that the xcoordinate is 3 or 3. The center lies in the third quadrant. So x = 3 The center...

geometry2We'll have to use the law of cosines to determine the length of the side "a". a^2 = b^2 + c^2  2b*c*cos (b,c) (1) We know that the side "a" is facing to the angle A, then the side "b" is facing to...

geometry2Since the lengths of the 3 sides are given, we'll use the law of cosines to determine the measure of the largest angle. The largest angle is the opposite angle to the largest length of triangle....

geometry2We know that an isosceles triangle has 2 equal angles. Since the given angle is an obtuse angle, then the other 2 angles are equal and they are of x degrees. We know that the sum of all angles of a...

geometry2We'll consider the three angles of triangle as: A,B,C. By definition, the sum of angles of a triangle is 180 degrees. A+B+C = 180 degrees We'll consider A as being the obtuse angle of the triangle...

geometry2The distance between any two points (x1 , y1) and (x2 , y2) is given as sqrt ((x1  x2)^2 + (y1  y2)^2) Here the points are ( 2x+3, 8) and (2x, 4) The distance between the two is sqrt [(2x + 3 ...

geometry2Area and perimeter have different units, so I'll consider only their numeric values. Let the side of the square be S. The perimeter is 4S and the area is S^2 As the area is 60 more than the...

geometry2Area and perimeter have different units, so I'll consider only their numeric values. Let the side of the square be S. The perimeter is 4S and the area is S^2 As the area is 60 more than the...

geometry2For the triangle ABC AB = 6, B=pi/4, C=pi/6. As the angles of a triangle have a sum of pi. A = 7*pi/12 Use the property sin A/a = sin B/b = sin C/c c = 6, C = pi/6, B = pi/4 and A = 7*pi/12 =>...

geometry2The center of the circle is (1,1). The point (3, 5) lies on the circle. The distance from (3,5) to (1,1) is the radius of the circle. This is equal to sqrt[(3  1)^2 + (5  1)^2] = sqrt [ 4 + 16] =...

geometry2Tangent.Find the equation of the tangent to the curve y = x^3  7x^2 + 14x  8 at the point where...For the equation of the tangent we need the slope of the tangent and one point it passes through. The slope of a tangent to any curve at a point is the value of the first derivative at that point....

geometry2The equation of a line between points (x1, y1) and (x2, y2) is: (y  y1)/(x  x1) = (y2  y1)/(x2  x1) Substituting the values given, the equation of the line is: (y + 5)/(x  7) = (1 + 5)/(3 ...

geometry2The general equation of a circle with center (a,b) and radius r is: (x  a)^2 + (y  b)^2 = r^2 Here the center is (0,0) and the radius is 3. Substituting the values x^2 + y^2 = 9 The equation of...

geometry2To verify if the given lines are parallel, perpendicular or neither, we'll have to put them first, in the point slope form: y = mx + n We'll start with the first equation: 4x+5y=198 We'll keep 5y...

geometry2To determine the length of the side BC, we'll use the law of sines. Since BC is the opposite to the angle A, we'll get: BC/sin A = AC/ sin B We'll determine the measure of the angle B, based on...

geometry2Since BM is the opposite side of the angle A = pi/2, that means that it is hypotenuse of the right angle triangle ABM. To determine BM, we need to calculate the missing length AC. We'll apply...

geometry2We have to find vector v if u*v=15, w*v=17 and u=5i+2j, w=ij Let v = ai + bj u*v = 15 = 5a + 2b ...(1) w*v = 17 = a  b ...(2) (1) + 2*(2) => 5a + 2b + 2a  2b = 34 + 15 => 7a = 49 => a =...

geometry2The power of M with respect to circle C is: p(M) = d^2  r^2 d  is the distance from M to the center of the circle C. We'll calculate d^2 = 8^2 + 3^2 d^2 = 64 + 9 d^2 = 73 p(M) = 73  25 p(M) = 48...

geometry2Let the linear function be f(c) = ax + b. y = ax + b is in the slope intercept form with the slope being a. We have f(2) = 6 and f(2) = 4 2a + b = 6 ...(1) 2a + b = 4 ...(a) (1)  (2) => 4a...

geometry2Let x be one side of the square. The area of the square is: A = x^2 The perimeter of the square is: P = 4x Now, we'll write mathematically the condition given by enunciation: x^2 = 4x  4 (area is...

geometry2The curve defined by the equation x^2 + y^2  16 = 0 can be written as x^2 + y^2  16 = 0 => (x  0)^2 + (y  0)^2 = 4^2 This is the equation of a circle with center at (0,0) and a radius of 4....

geometry2To find the slope, we need two points from the line. If x = 0, 2y = 12 and y = 6. This means that one of our points is (0,6) If y = 0, 4x = 12 and x = 3. This means that another point is (3,0)....

geometry2To find the slope of a line, we use the formula m = (y1  y2)/(x1  x2). In this case, your p value is x and your q value is y. We know that, for any number, q1  q2 is going to equal 4. This is...

geometry2GeometryIf the hypothenuse of right triangle of 26 cm long and one cathetus 14 cm longer than the...It is given that the hypotenuse of a right triangle is 26 cm long and one leg is 14 cm longer than the other. Let the length of the shorter leg be x , the other leg is x + 14 AS it is a right...

geometry2We have the points A(2,2) B(1,1) C(1,4) and D(x,5) and we need to find x if AB and CD are parallel. The slope of AB is (1+2)/(12) = 3/1 = 3 The slope of CD is (54)/(x  1) = 1/(x  1) For...

geometry2Let the smaller sides of the triangle have a length a and b. The length of the hypotenuse is sqrt( a^2 + b^2) The area of the triangle is (1/2)*a*b = 6 => ab = 12 => a = 12/b The perimeter is...

geometry2Find the value of m if the perpendicular bisector of the line that passes through the point (6,8)...We know that the slope of the perpendicular bisector is the opposite reciprocal of the slope containing the two given points. Therefore, the slope of the line containing the two given points is...

geometry2The equation of a circle is (x  a)^2 + (y  b)^2 = r^2 As we know three points through which the circle passes, we can create three equations. (2 , 4) (2  a)^2 + (4  b)^2 = r^2 ...(1) (3 ,...

geometry2The general equation of a circle has three variables, if the center is (a, b) and r is the radius: (x  a)^2 + (y  b)^2 = r^2. You have provided two points through which the circle passes (0,5)...

geometry2What is the value of constant k if the perpendicular bisector of the segment with endpoints (k,0)...The perpendicular bisector of the segment with endpoints (k,0) and (4,6) has a slope 3. This gives the slope of the line segment with end points (k,0) and (4,6) as 1/3. We get this as the product...

geometry2Find the slope of the line that is perpendicular to the line that passes through the points (1,3)...The slope of two perpendicular lines m1 and m2 are related as m1* m2 = 1. The slope of the line through (1,3) and ( 2,6) is : m = (6  3)/(2  1) => m = 3 A line perpendicular to this line has...

geometry2The mid point of a line joining the points (x1, y1) and ( x2, y2) is given by [(x1 + x2) / 2 , (y1 + y2)/2] For the side, BC the coordinates of B are (7 , 3) and those of C are ( 5, 7). The mid...

geometry2We have the function f(x) = x^2. The points given to us are (t , f(t)) and (t+h , f(t+h)) or (t , t^2) and ((t + h) , (t + h)^2) The gradient between these points is =>[ (t + h)^2  t^2] / [ t +...

geometry2We have to find the straight line passing through the points ( 3,2) and ( 5,8) The equation of a line passing through the points ( x1, y1) and ( x2, y2) is given by ( y  y1) = [ ( y2  y1)/(x2 ...

geometry2What are the values of parameter m if the vertex of parabola y = x^22(m1)*x+m1 is on the first...Firts, we'll determine the coordinates of the vertex of the parabola. V(b/2a ; delta/4a) deta = b^2  4ac a,b,c, are the coefficients of the quadratic. a = 1 , b = 2(m1) , c = m1 xV =...

geometry2Two lines are parallel if their slopes are equal or the ratios of correspondent coefficients are equal. We'll form the ratios of the correspondent coefficients: (t3)/1 = 2/(t+1) We are applying...

geometry2Given the lines: f(x)= 2x  1 g(x)= 4x + 1 In order to find a point on both lines, then we need to determine where the lines intersects. To find intersection points we need to determine x values...

geometry2The median AE is the line joining the point A(1,2) to the point between the points B(2, 3) and C(2 , 5). Note: I am providing the equation of the median AE which I believe is what you want. The...