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).
