# Three vertices of a rectangle are (3, 2), (-4, 2) and (-4, 5). Plot these points and find the coordinates of the fourth vertex

**Solution:**

Given, three vertices of a rectangle are (3, 2), (-4, 2) and (-4, 5)

We have to plot the points and find the coordinates of the fourth vertex.

Let the point (3, 2) be A

The x-coordinate is positive and the y-coordinate is positive

Therefore, the point A lies on the first quadrant

Let the point (-4, 2) be B

The x-coordinate is negative and the y-coordinate is positive

Therefore, the point B lies on the second quadrant

Let the point (-4, 5) be C

The x-coordinate is negative and the y-coordinate is positive

Therefore, the point C lies on the second quadrant

On plotting the points A, B and C

To find the fourth vertex D of the rectangle ABCD

We know that the opposite sides of a rectangle are equal.

So the abscissa of A is equal to abscissa of D

So, abscissa of D = 3

The ordinate of C is equal to ordinate of D

So, ordinate of D = 5

Therefore, the coordinates of D are (3, 5)

**✦ Try This:** By taking rectangular coordinate axis plot the points 0 (0,0), P (3, 0) and R(O, 4). If OPQR is rectangle, then find coordinates of Q.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 3

**NCERT Exemplar Class 9 Maths Exercise 3.4 Sample Problem 1**

## Three vertices of a rectangle are (3, 2), (-4, 2) and (-4, 5). Plot these points and find the coordinates of the fourth vertex

**Summary:**

Three vertices of a rectangle are (3, 2), (- 4, 2) and (- 4, 5). On plotting these points, the coordinates of the fourth vertex are (3, 5)

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