Vertices of a square

Geometry Level 1

$ABCD$ are 4 vertices of a square. Given that $A = (3, 5)$ , $B = (8, 13)$ , $C = (16, 18 )$ , and $D = (x,y)$ , what is the value of $x + y$ ?

The answer is 21.

1 solution

Arron Kau Staff
May 13, 2014

The center of the square is the midpoint of $AC$ , which is $\left( \frac{3+16}{2}, \frac{5+18}{2} \right)$ . This is also the midpoint of $BD$ , which gives us that $\left( \frac{3+16}{2}, \frac{5+18}{2} \right) = \left(\frac{ 8+x}{2} , \frac{13+y} {2} \right)$ .

Hence, we obtain $x = 11, y = 10$ , so $x + y = 21$ .

Vertices of a square

The answer is 21.

1 solution

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