Question

A rectangle has vertices at these coordinates. (1, 2) , (3, 2) , (1, −8) What are the coordinates of the fourth vertex of the rectangle? Enter the coordinates in the boxes.

Answer 1

(3, -8)

Explanation:

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Answer 2

The coordinates of the fourth vertex of the rectangle is (3,-8).

Explanation:

It is given that a rectangle has vertices at these coordinates. (1, 2) , (3, 2) , (1, −8).

Let the coordinates of the fourth vertex of the rectangle be (x,y).

The diagonals of rectangle intersect each other at their midpoint.

Plot these points on a coordinate plane. From the graph it is noticed that the end point of one diagonal are (3, 2) and (1, −8).

`Midpoint=((3+1)/(2),(2-8)/(2))=(2,-3)`

The end point of second diagonal are (1, 2) and (x,y).

`Midpoint=((1+x)/(2),(2+y)/(2))`

Since the diagonals of rectangle intersect each other at their midpoint, therefore

`((1+x)/(2),(2+y)/(2))=(2,-3)`

On comparing both the sides,

`(1+x)/(2)=2\Rightarrow 1+x=4\Rightarrow x=3`

`(2+y)/(2)=-3\Rightarrow 2+y=-6\Rightarrow y=-8`

Therefore the coordinates of the fourth vertex of the rectangle is (3,-8).