Question

The coordinates of the three given vertices of a rectangle ABCD are given. By plotting the given points & find the coordinates of the fourth vertex: $A\left( 4,2 \right)\text{ }B\left( -2,2 \right)\text{ }D\left( 4,-2 \right)$
A.$\left( 2,-2 \right)$
B.$\left( -2,-2 \right)$
C.$\left( 2,2 \right)$
D.$\left( -2,2 \right)$

Answer 1

Hint: Plot the given points on a graph paper and use the following properties of the rectangle to find the 4th coordinate (say point C )
1. Opposite sides of a rectangle are equal in length.
2. All the angles in a rectangle are right angles.

Complete step-by-step answer:
Using the given points$A\left( 4,2 \right)\text{ }B\left( -2,2 \right)\text{ }D\left( 4,-2 \right)$
We'll plot a graph.

After plotting the given points, join A and B; A and D
From the graph it is clear that AB = 6 units and AD = 4 units.
Therefore, the vertical distance = AD = 4 units should be the same in BC. Hence we get using the property of the rectangle that opposite sides are the same AD = BC = 4 units.
Now going 4 units downwards from point B we get the ordinate of point C as $-2$
Also, horizontal Distance = AB = 6 units.
And using the property of rectangle that opposite sides are same we get,
AB = CD = 6 units
So we move 6 units from D towards origin and get abscissa of C as $-2$
So the coordinates of the 4th point C will be $\left( -2,-2 \right)$
Hence, the correct answer is $\left( -2,-2 \right)$ which is option B.

Note: Rectangle is a parallelogram where opposite sides are parallel as well as equal to each other. All the interior angles are right angles.