Question

Find equation of diagonal of rectangle whose sudes are x=-1 x=4 y =-1 y=2

Answer 1

From these lines we can find out that the four vertices of the rectangle have the coordinates (-1, -1), (-1, 2), (4, -1), (4, 2).

Consider the points (-1, -1) and (4, 2). They're diagonally opposite to each other.

Slope of the diagonal joining these points,

(2 + 1) / (4 + 1) = 3 / 5

Now we have the equation with (4, 2).

y - 2 = 3(x - 4) / 5

y - 2 = (3x - 12) / 5

5y - 10 = 3x - 12

3x - 5y - 2 = 0

So we got equation for a diagonal. Let's find the equation of the other.

This diagonal join the points (-1, 2) and (4, -1). So we have the slope,

(- 1 - 2) / (4 + 1) = - 3 / 5

Now the equation with (-1, 2),

y - 2 = - 3(x + 1) / 5

5y - 10 = - 3x - 3

3x + 5y - 7 = 0