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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)

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 class=

Sagot :

Start with two vertex points from one side of the rectangle:
(4, 0) and (2, -3).
Subtract the X coordinates:  4 - 2 = 2
Subtract the Y coordinates:  0 - -3 = 3
Now, start with the third vertex point that is given:
(-2,4).
The differences for the X & Y coordinates between the third vertex point and the fourth vertex point will be the same as the differences between the 1st and 2nd points, so start with the 3rd point X coordinate and subtract 2 from it to get the X coordinate for the fourth point:
-2 - 2 = -4.
Then, take the 3rd point Y coordinate and subtract 4 to get the Y coordinate for the fourth point:
4 - 3 = 1
So, your fourth vertex point is (-4, 1).
See the attached picture.
This works because each of the two sets of sides of a rectangle are parallel to each other.  
View image tjshoup
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