Question

Three vertices of a rectangle are given. Find the coordinates of the fourth vertex. . . (–2, 4), (4, 0), (2, –3). . A) (–4, –1). B) (–4, 0). . C) (–4, 1). D) (–4, 2).

Answer 1

There are several ways to find the coordinates of the fourth vertex. This is one of them.
The slope of AB:
m AB = 0-(-4)/4-(-2) = -4/6 = -2/3
m AB = m CD
CD: y = m x+b
-3 = 2 · ( -2/3 ) + b
- 3 = -4/3 + b
b = - 3 + 4/3 = -5/3
CD : y = -2/3 x - 5/3
m BC = 0-(-3) / 4 - 2 = 3/2
m BC = m AD = 3/2
AD : y = m x + b
4 = 3/2 · ( -2 ) + b
4 = - 3 + b
b = 7
AD : y = 3/2 x + 7
We will find the point of intersection of the lines AD and CD:
3/2 x + 7 = - 2/3 x - 5/3 / · 6
9 x + 42 = -4 x - 10
13 x = -52
x = - 4
y = 3/2 · ( -4 ) + 7 = -6 + 7 = 1
Answer: C ) ( - 4, 1 )