Question

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

A) 32 units
B) 34 units
C) 64 units
D) 68 units

Answer 1

Distance between points A and B is,
`√(68)` units

Explanation:

Given the coordinates point :

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

Using distance formula:

i,e

`D = √((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= √(4-4)^2+(0-2)^2)`

`AC= √((0)^2+(-2)^2)`

`AC= √(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= √(4+4)^2+(0-0)^2)`

`BC= √(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= √(68)` units.

Therefore, the distance between points A and B is,
`√(68)` units