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

Solution:

{ Refer to the attachment for the graph missing in the question }

Here the coordinates of D and F are (- 1, - 3) and (2, 3) respectively.

The equation of the line DF is

(y - 3) / (3 + 3) = (x - 2) / (2 + 1)

or, (y - 3) / 6 = (x - 2) / 3

or, y - 3 = 2 (x - 2)

or, y - 3 = 2x - 4

or, y - 2x = - 1 ..... (1)

Then the equation of the line parallel to DF is

y - 2x = k ..... (2)

The coordinates of the point G is (- 4, - 4). From (2), we get

- 4 + 8 = k

or, k = 4

So the equation of the line through G parallel to DF is

y - 2x = 4

or, (y - 2x) / 4 = 1

or, y/4 - 2x/4 = 1

or, y/4 + x/(- 2) = 1

or, x/(- 2) + y/4 = 1

So the line through G parallel to DF intersects the x-axis at (- 2, 0) and y-axis at (0, 4)

Hence the required point on y-axis is (0, 4)