Line d1 passes through the points (-2,0) and (0,a). Line d2 passes through the points (4,0) and (6,2). What value of a makes the two lines parallel?A) 1/2 B) -2 C) 2 D) -1/2 E) 0
We have two lines, one passing through (-2,0) and (0,a) and the other passing through (4,0) and (6,2)
Now the line through (-2,0) and (0,a) is y-0 = [(a-0)/(0+2)] (x+2).
y = (a/2)(x+2)
The slope of this line is a/2.
The other line is
y-0 = [(2-0)/(6-4)](x-4)
=> y= (2/2)(x-4)
The slope of this line is 1
As the two lines are parallel, the slope has to be equal.
Therefore a/2 = 1 => a = 2
The required value of a is 2. The correct option is C.
The lines d1 and d2 passes through (-2,0) and (0,a) ; and (4,0) and (6,2).
The slope m of the lines passing through (x1,y1) and (x2, y2) is given by:
m = (y2-y1)/(x2-x1).
So the slope m1 of the line d1 is given by:
m1 = (a-0)/(0-(-2)) = a/2.
The slope m2 of the line d2 is given by:
m2 = (2-0)/(6-4) = 2/2 = 1.
So if d1 and d2 are ||, then their slopes should be equal.
So m1 = m2 .
Or a/2 = 1. So a = 2.
Therefore if a = 2, the lines d1 and d2 are parallel.
We'll put the equations of the 2 lines in the standard form.
y = mx + n
m is the slope of the line
n is the y intercept
For d1 and d2 to be parallel, their slopes have to be equal.
m1 = m2
We'll write the equation of the line d1 that passes through (-2,0) and (0,a).
(0+2)/(x+2) = (a-0)/(y-0)
2/(x+2) = a/y
We'll cross multiply and we'll get:
a(x+2) = 2y
We'll remove the brackets and we'll use the symmetric property:
2y = ax + 2a
We'll divide by 2:
y = ax/2 + a
m1 = a/2
We'll write the equation of the line d2 that passes throug the points (4,0) and (6,2):
(6-4)/(x-4) = (2-0)/(y-0)
2/(x-4) = 2/y
We'll divide by 2 and we'll cross multiply and we'll get:
x - 4 = y
We'll use the symmetric property:
y = x - 4
m2 = 1
The condition for d1|| d2:
m1 = m2
a/2 = 1
a = 2