Question

Which point on the y-axis lies on the line that passes through point G and is parallel to line DF?

(–2, 0)
(0, –2)
(0, 4)
(4, 0)

Answer 1

I just took the test, its c.

Answer 2

Given that the line passing through the required point is parallel to line DF, then the slope of the line will be equal to the slope of line DF.

Recall that the slope, m, of a line passing through two points
`(x_1,y_1)` and
`(x_2,y_2)` is given by

`m= (y_2-y_1)/(x_2-x_1)`

Notice that line DF passes through the ponts (-1, -3) and (2, 3), thus the slope of line DF is given by

`m= (3-(-3))/(2-(-1)) = (3+3)/(2+1) = (6)/(3) =2`

Thus the slope of the line passing through the required point is 2

Since, the required point is on the y-axis, the point will be of the form (0, b) and it's given that the line also passes through point G(-4, -4).

Thus, we have,

`(b-(-4))/(0-(-4)) =2 \\ \\ (b+4)/(4) =2 \\ \\ b+4=8 \\ \\ b=4`

Therefore, the point on the y-axis that lies on the line that passes through point G and is parallel to line DF is point (0, 4).