Question

Plot the following points to create a rectangle.

Find the missing vertex.(5.3): (-5,3): (-5.-1) *

Answer 1

(5, -1)

Explanation:

The three coordinates of a triangle are given as:

(5,3), (-5,3), (-5,-1).

To find:

The missing vertex = ?

Solution:

Let us label the vertices:

A (5,3),

B(-5,3),

C(-5,-1).

Let the missing vertex be (
`x, y`).

Let us recall the properties of a rectangle.

The opposite sides of the rectangle are equal and parallel to each other.

Let us consider the side AB, we can see that only x coordinate is changed from A to B.

Let us consider the side BC, we can see that only y coordinate is changed from B to C.

A and B are adjacent vertices.

Similarly the opposite vertices will be C and D.

Same pattern will be followed in CD as that of AB.

x coordinate will be changed by same difference as that of AB.

Change in x coordinate from D to C =
`-5-x`

Change in x coordinate from A to B =
`-5-5 =-10`

Equating them:

`-5-x=-10\\\Rightarrow x = 5`

Same pattern is followed in BC and AD.

Their change in y coordinate will be same.

`-1-3=y-3\\\Rightarrow y =-1`

Missing vertex is (5, -1).

Please refer to the attached image for the rectangle.