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

Answer:

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

Step-by-step 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).

$Midpoint=(\frac{3+1}{2},\frac{2-8}{2})=(2,-3)$

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

$Midpoint=(\frac{1+x}{2},\frac{2+y}{2})$

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

$(\frac{1+x}{2},\frac{2+y}{2})=(2,-3)$

On comparing both the sides,

$\frac{1+x}{2}=2\Rightarrow 1+x=4\Rightarrow x=3$

$\frac{2+y}{2}=-3\Rightarrow 2+y=-6\Rightarrow y=-8$

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

Answer 2

Answer:

(3, -8)

Step-by-step explanation:

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