Question

Find the fourtg vertex of square whose consecutive vertices are (2,1),(7,4),(2,5)

Answer 1

Answer:

The fourth vertex is (-3,2)

Step-by-step explanation:

Given three consecutive vertices of square (2,1), (7,4), (2,5). we have to find the fourth vertex of square.

As diagonals of square bisect each other.

∴ mid-point of AC is also the mid point of BD

By mid point formula

$(\frac{7+x}{2}, \frac{4+y}{2})=(\frac{2+2}{2}, \frac{1+5}{2})$

⇒ $(\frac{7+x}{2},\frac{4+y}{2})=(2,3)$

⇒ $\frac{7+x}{2}=2, \frac{4+y}{2}=3$

⇒ $7+x=4, 4+y=6$

⇒ x=-3 and y=2

Hence, the fourth vertex is (-3,2)