Question

Apply the Pythagorean Theorem to find the distance between points A and B.

Answer 1

Answer:

Distance between points A and B is, $\sqrt{68}$ units

Step-by-step explanation:

Given the coordinates point :

A = (4 , 2) , B = (-4, 0) and C = (4, 0)

Using distance formula:

i,e

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

First calculate the length of AC ;

where A = (4, 2) and C = (4, 0)

then using distance formula;

$AC= \sqrt{4-4)^2+(0-2)^2}$

$AC= \sqrt{(0)^2+(-2)^2}$

$AC= \sqrt{4}$ = 2 units.

Similarly, calculate the length of BC;

Using distance formula on the given points B =(-4, 0) and C = (4, 0)

then;

$BC= \sqrt{4+4)^2+(0-0)^2}$

$BC= \sqrt{8)^2}$ = 8 units.

Now, using Pythagorean theorem in triangle ACB; to find the distance AB

$AB^2=AC^2+BC^2$

Substitute the values of AC = 2 units and BC = 8 units;

$AB^2 =2^2+8^2$

Simplify:

$AB^2 =4+64 = 68$

or

$AB= \sqrt{68}$ units.

Therefore, the distance between points A and B is, $\sqrt{68}$ units