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.

Question

asked Nov 15, 2018 143k views

2 Answers

Kalilah · Answer 1 · 2018-11-20T09:51:05+0000

Answer:

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).