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

Plot the points, and it should be quite evident where the 4th vertex should go.

Answer 2

The missing point will have the same relationship to the point on the upper left as the bottom point on the right has to the point on the upper right ((4,0))

Answer 3

This is one of many ways to proceed.
First find the slope of line AB; (yB - yA)/(xB - xA)= -4/6 = -2/3
Consequently, the slope of line AD is (3/2) (AD perpendicular to AB)
Equation of the line DA that passes by point A(-2, 4)
y = 3x/2 + b --> 4 = 3(-2)/2 + b -> b = 4 + 3 = 9
Equation of line DA: y = 3x/2 + 7.(1)
Slope of line CD parallel to AB: -2/3.
Equation of line CD that passes at point C (2, -3)
y = -2x/3 + b --> -3 = -4/3 + b -> b = -3 - 4/3 = -5/3
Equation of line CD: y = -2x/3 - 5/3.(2)
Write that D is the intersection the line AD(1) and line CD (2):
3x/2 + 7 = -2x/3 - 5/3 --> 13x/6 = -26/3 --> x = -4
Coordinates of D: x = --- and y =.....