Question

Rectangle ABCD has a perimeter of 22 units. The coordinates of the rectangle’s vertices are A(−4, 5) , B(3, 5), C(3, x), and D(−4, x). Which could be the value of x?

Answer 1

• x = 1 or x = 9

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The distance between A and B is the difference of x-coordinates, as y-coordinates are same:

• 3 - (-4) = 3 + 4 = 7 units

It means parallel side has same length.

Using perimeter we can find the adjacent side length:

• AD = BC = (22 - 2*7)/2 = 8/2 = 4 units

Since AB is horizontal, AD and BC are vertical segments.

Position of C and D could be above or below the segment AB.

If above AB, then coordinates are:

• C(3, x) = C(3, 5 + 4) = C(3, 9)
• D(-4, x) = D(-4, 5 + 4) = D(-4, 9)

If below AB, then coordinates are:

• C(3, x) = C(3, 5 - 4) = C(3, 1)
• D(-4, x) = D(-4, 5 - 4) = D(-4, 1)

See attached for better visual.