Question

The eqution of the diagonal of a parallelogram is 3y=5x +k. The two opposite vertices of a parallelogram are the points (1,-2), (-2,1).Find the value of k

Answer 1

Answer:

$k = 1$

Step-by-step explanation:

Given

$3y = 5x + k$

Opposite points: $(1,-2)$ and $(-2,1)$

Required

Find k

First, calculate the midpoint of the opposite points.

$(x,y) = 0.5(x_1 + x_2,y_1 + y_2)$

This gives:

$(x,y) = 0.5(1 -2,-2 + 1)$

$(x,y) = 0.5(-1,-1)$

Open bracket

$(x,y) = (-0.5,-0.5)$

The equation $3y = 5x + k$ becomes:

$3 * -0.5 = 5 * -0.5 + k$

$-1.5 = -2.5 + k$

Solve for k

$k = 2.5-1.5$

$k = 1$