Question

7. The coordinates of the vertices of a rectangle are go

I 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

a. By Pythagorean Theorem:
`ET=√(113)`

b. 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=7^2+8^2`

`ET^2=49+64`

`ET^2=113`

Take positive square root to obtain:

`ET=√(113)`

b. The distance formula is given by:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

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)`