Question

The fourth vertex of the square whose consecutive vertices are (2,1),(7,4),(-2,5) is

Answer 1

therefore,the fourth vertex of the square whose consecutive vertices is(-7,2)

Answer 2

Hence the fourth vertex of the square is (2,1)

Step-by-step explanation:

Given:

Let ABCD be the rectangle

We have A=(2,1), B=(7,4), C=(-2,5) and let D=(x,y)=?

Let E be the midpoint of AC i.e.midpoint of (2,1) and (-2,5) by the midpoint formula, we get        

E =$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

E =$(\frac{2+7}{2},\frac{1+4}{2})$

E =$(\frac{9}{2},\frac{5}{2})$

Midpont of BD where D is (x,y), B=(7,4) the midpoints are coincident, so midpoint of both AC and BD is E.

So therefore,

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=E$

$(\frac{x_1+7}{2},\frac{y_1+4}{2})=(\frac{9}{2},\frac{5}{2})$

So, $\frac{x_1+7}{2}=\frac{9}{2}$ and  $\frac{y_1+4}{2}=\frac{5}{2}$

${x_1+7}=\frac{9\times2}{2}$ and  ${y_1+4}=\frac{5\times2}{2}$

${x_1+7}=9$ and  ${y_1+4}=5$

${x_1}=9-7$ and  ${y_1}=5-4$

${x_1}=2$ and  ${y_1}=1$

Hence D(x,y)=(2,1).