Question

The coordinates of the vertices of a rectangle are given by R(- 3, - 4), E(- 3, 4), C (4, 4), and T (4, - 4). Plot these points on the coordinate plane at the right and connect them to draw the rectangle. Then connect points E and T to form diagonal _ET . a. Use the Pythagorean Theorem to find the exact length of _ET . b. How can you use the Distance Formula to find the length of _ET ? Show that the Distance Formula gives the same answer.

Answer 1

By Pythagorean theorem:
`ET=√(113)`

By distance formula:
`ET=√(113)`

Explanation:

The given rectangle has vertices R(-3,-4), E(-3, 4), C(4,4), and T(4-4).

The points have been plotted on the coordinate plane as shown in the attachment.

A. Using the Pythagoras Theorem;

`ET^2=EC^2+CT^2`

We substitute the side lengths to obtain:

`ET^2=EC+CT^2`

`ET^2=49+64`

`ET^2=113`

Take positive square root to obtain:

`ET=√(113)`

B. The distance formula is given by:

`d=\sqrt{(x_(2)-x_{1)^2+(y_(2)- y_(1) )`

The endpoints of ET are at E(-3,4) and T(4,-4).

Using the distance formula;

`ET=√(4--3)^2+(-4-4)^2)`

`ET=√((7)^2) +(-8)^2`

`ET=√(49+64)`

`ET=√(113)`