Question

Three of the vertices of a square are the points whose coordinates are (2, 3), (2, 6), and (5, 3). What are the coordinates of the fourth vertex?

Answer 1

I believe the correct answer is (5,6).
I hope this helps!
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Answer 2

Answer:

Coordinate of 4th vertex is (5,6)

Step-by-step explanation:

Given three of the vertices of a square are the points whose coordinates are (2, 3), (2, 6), and (5, 3).

we have to find the coordinates of the fourth vertex.

By mid-point formula, if (a,b) and (c,d)  are the vertices of line segment then the coordinates of mid-point are

$(\frac{a+b}{2},\frac{c+d}{2})$

As the diagonals of square are equal and bisect each other therefore the mid point of both the diagonal are same.

∴ mid-point of AC=mid-point of BD

$(\frac{2+5}{2},\frac{6+3}{2})=(\frac{2+x}{2},\frac{3+y}{2})$

$(\frac{7}{2},\frac{9}{2})=(\frac{2+x}{2},\frac{3+y}{2})$

Comparing

2+x=7 and 3+y=9

x=5 and y=6

Hence, coordinate of 4th vertex is (5,6)