Question

Use the distance formula to find the lengths of the sides (AC and AE) that include the overlapping angle

The length AC is___ square root of 2
A. 2
B. 4
C.8
D.16
The length AE is ___ square root of 2
A.2
B.4
C.8
D.16

Answer 1

Explanation:

AC is 2

AE is 4

Answer 2

Part 1) Option A. 2

Part 2) Option B. 4

Explanation:

we know that

The formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

step 1

Determine distance AC

we have

A(3,1),C(5,3)

substitute in the formula

`d=\sqrt{(3-1)^(2)+(5-3)^(2)}`

`d=\sqrt{(2)^(2)+(2)^(2)}`

`d=√(8)\ units`

simplify

`AC=2√(2)\ units`

therefore

The length AC is 2 square root of 2 units

step 2

Determine distance AE

we have

A(3,1),E(7,5)

substitute in the formula

`d=\sqrt{(5-1)^(2)+(7-3)^(2)}`

`d=\sqrt{(4)^(2)+(4)^(2)}`

`d=√(32)\ units`

simplify

`AE=4√(2)\ units`

therefore

The length AE is 4 square root of 2 units