# The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices

**Solution:**

Let's draw a figure of a square with the two opposite vertices (-1, 2) and (3, 2),

Let ABCD be a square having known vertices A (- 1, 2) and C (3, 2) as vertices A and C respectively.

Let B(x_{1}, y_{1}) be one unknown vertex

We know that the sides of a square are equal to each other.

Therefore, AB = BC

By Using Distance formula to find distance between points AB & BC,

√ [{x - (-1)}^{2} + (y - 2)^{2}] = √ [(x - 3)^{2} + (y - 2)^{2}]

x^{2} + 2x + 1 + y^{2} - 4y + 4 = x^{2} + 9 - 6x + y^{2} + 4 - 4y (By Simplifying & Transposing)

8 x_{1} = 8

x_{1} = 1

We know that in a square, all interior angles are 90 degrees.

In ΔABC

AB^{2} + BC^{2} = AC^{2} [By Pythagoras theorem]

The distance formula is used to find the distance between AB, BC, and AC

[{x - (-1)}^{2} + (y - 2)^{2}] + [(x - 3)^{2} + (y - 2)^{2}] = [3 - (-1)]^{2} + [ 2 - 2 ]^{2}

4 + y_{1}^{2} + 4 - 4y_{1} + 4 + y_{1}^{2} - 4y_{1} + 4 = 16

2y^{2} + 16 - 8y = 16

2y^{2} - 8y = 0

y_{1} (y_{1} - 4) = 0

y_{1} = 0 or 4

Hence the required vertices are B (1, 0) and D (1, 4).

**Video Solution:**

## The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices

### Maths NCERT Solutions Class 10- Chapter 7 Exercise 7.4 Question 4:

The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices

The two opposite vertices of a square are (- 1, 2) and (3, 2). Then the coordinates of the other two vertices are B (1, 0) and D (1, 4)