Question

From the adjacent figure:
(i) Write the coordinates of the points A, B, and

(ii) Write the slope of the line AB.
(iii) Line through C, drawn parallel to AB, intersects Y-axis at D. Calculate the co-ordinates of D.

Answer 1

(i) Coordinates of the points A, B and C are (1, 3), (-3, -2) and (3, 0) respectively.
(ii) Slope of AB = `(-2 - 3)/(-3 - 1) = (5)/(4)`.
(iii) Line through C(3, 0) and parallel to AB.
∴ Slope = `(5)/(4)`.
∴ Equation to the line is
y - y₁ = m(x - x₁)
y - 0 = `(5)/(4)(x - 3)`
4y = 5x - 15
This line intersects Y-axis at D.
∴ On solving
4y = 5x - 15
and x = 0,  ...(Equation to Y-axis)
We get,  4y = -15
y = `-(15)/(4)`
∴ Coordinates of point D are `(0, -15/7)`.