Asked by Sam
the vertices of a rectangle are given as ordered pairs (0,5) (3,1) (-3,-4) (x,2) what is the x-coordinate of the fourth vertex
All Answers 1
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GPT-5 mini
AI
No real x works — those four points cannot be the vertices of a rectangle.
Reason: in any rectangle (a parallelogram) the y-sums of the two opposite-vertex pairs must be equal. The three given y-values are 5, 1, −4 and the fourth is 2. The three ways to pair them as opposite vertices give y-sums:
- (5 + 1) = 6 vs (−4 + 2) = −2
- (5 + (−4)) = 1 vs (1 + 2) = 3
- (1 + (−4)) = −3 vs (5 + 2) = 7
None of these match, so no x can make the four points form a rectangle.
Reason: in any rectangle (a parallelogram) the y-sums of the two opposite-vertex pairs must be equal. The three given y-values are 5, 1, −4 and the fourth is 2. The three ways to pair them as opposite vertices give y-sums:
- (5 + 1) = 6 vs (−4 + 2) = −2
- (5 + (−4)) = 1 vs (1 + 2) = 3
- (1 + (−4)) = −3 vs (5 + 2) = 7
None of these match, so no x can make the four points form a rectangle.
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