Question

Two of the vertices of a rectangle are (1, −6) and (−8, −6). If the rectangle has a perimeter of 26 units, what are the coordinates of its other two vertices?

Answer 1

Answer:
`(x_1,y_1)=(1,-2)`

`(x_2,y_2)=(-8,-2)`

Explanation:

Given

Co ordinates of vertices(1,-6) and (-8,-6)

When two points is given then Length of two points is given by

`L=√(\left ( x_2-x_1\right )^2+\left ( y_2-y_1\right )^2)`

`L=√(\left ( 1-\left ( -8\right )\right )^2+\left ( -6+6\right )^2)`

`L=√(9^2)=9 units`

Perimeter of rectangle is =26 units

Let the other side be x

thus

`2\left ( x+9\right )=26`

x+9=13

x=4 units

therefore to get the other two co ordinates

such that the length of that side is 4 units is

`(x_1,y_1)=(1,-2)`

`(x_2,y_2)=(-8,-2)`

Horizontal distance will remain same only vertical distance will change in given co ordinates to obtain the remaining two co ordinates

To verify the above two distance between two points must be 13 units