geometry2 Questions and Answers

geometry2

In Geometry, there are various possible angle sizes and each angle falls into the category of either an acute angle (smaller than 90 degrees), a right angle (90 degrees), an obtuse angle (bigger...

Latest answer posted February 15, 2016, 6:38 am (UTC)

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geometry2

We 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)/(1-2) = 3/-1 = -3 The slope of CD is (5-4)/(x - 1) = 1/(x - 1) For...

Latest answer posted April 13, 2011, 10:21 am (UTC)

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geometry2

We 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 -...

Latest answer posted February 17, 2011, 12:02 am (UTC)

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geometry2

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....

Latest answer posted May 6, 2011, 11:20 pm (UTC)

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geometry2

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...

Latest answer posted March 3, 2011, 12:48 am (UTC)

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geometry2

The 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...

Latest answer posted January 31, 2011, 3:51 pm (UTC)

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geometry2

Let 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...

Latest answer posted April 18, 2011, 12:10 am (UTC)

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geometry2

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...

Latest answer posted April 15, 2011, 9:11 pm (UTC)

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geometry2

The slope of a line passing through two points (x1 , y1) and (x2, y2) is m = (y2 - y1)/(x2 - x1) Here we have the points with the coordinates (p;q) and (p-4;q+4) . The slope of the line passing...

Latest answer posted April 14, 2011, 7:12 am (UTC)

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geometry2

When given the vertices's of rectangle, we can find the dimensions by using the distance between points formula. The distaqnce formula if given by : D = sqrt(x1-x2)^2 + (y1-y)^2 The formula you...

Latest answer posted February 4, 2011, 9:35 am (UTC)

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geometry2

Given 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...

Latest answer posted February 4, 2011, 9:28 am (UTC)

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geometry2

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

Latest answer posted May 11, 2011, 5:10 am (UTC)

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geometry2

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 =...

Latest answer posted May 11, 2011, 5:56 am (UTC)

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geometry2

We have to find vector v if u*v=15, w*v=17 and u=5i+2j, w=i-j 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 =...

Latest answer posted April 20, 2011, 8:36 am (UTC)

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geometry2

The 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] =...

Latest answer posted May 3, 2011, 12:45 pm (UTC)

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geometry2

For 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 =>...

Latest answer posted May 7, 2011, 12:11 am (UTC)

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geometry2

Area 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...

Latest answer posted May 3, 2011, 12:18 pm (UTC)

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geometry2

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...

Latest answer posted March 19, 2011, 8:06 pm (UTC)

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geometry2

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...

Latest answer posted February 26, 2011, 1:36 am (UTC)

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geometry2

Area 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...

Latest answer posted May 3, 2011, 12:33 pm (UTC)

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geometry2

The 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...

Latest answer posted February 21, 2011, 5:18 pm (UTC)

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geometry2

We 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 +...

Latest answer posted February 17, 2011, 12:08 am (UTC)

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geometry2

For 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...

Latest answer posted May 16, 2011, 11:48 pm (UTC)

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geometry2

The 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 -...

Latest answer posted April 29, 2011, 11:00 pm (UTC)

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geometry2

To 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)....

Latest answer posted April 13, 2011, 5:46 am (UTC)

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geometry2

The 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 -...

Latest answer posted May 7, 2011, 6:45 am (UTC)

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geometry2

The 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....

Latest answer posted April 14, 2011, 11:29 pm (UTC)

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geometry2

The 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...

Latest answer posted April 30, 2011, 9:23 pm (UTC)

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geometry2

Given a point on the line and a parallel line is enough information to determine the equation of the line. The equation of the line is: y-y1 = m (x-x1) We are given the point passes through the...

Latest answer posted February 4, 2011, 9:31 am (UTC)

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geometry2

The 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)...

Latest answer posted March 7, 2011, 10:41 pm (UTC)

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geometry2

The 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 ,...

Latest answer posted March 11, 2011, 12:59 am (UTC)

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geometry2

Let 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...

Latest answer posted March 28, 2011, 12:15 am (UTC)

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geometry2

The mid point between the points (x1, y1) and ( x2, y2) is given by [(x1 + x2)/2 , (y1 + y2)/2] Here we have the points A(-2 , 5) and B( 4 , 7) The middle point has the coordinates [( -2+4)/2 ,...

Latest answer posted January 21, 2011, 2:51 am (UTC)

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