Question

Find the distance between the given points A(–16, –15) and D(–2, –18)

Answer 1

`\Huge\boxed{\mathsf{\Rightarrow √(205)}}}`

Explanation:

TO FIND:

The distance between the give points of (-16, -15) and (-2, -18).

SOLUTIONS:

First, use slope formula.

SLOPE FORMULA:

`\Rightarrow \displaystyle \mathsf{(Y_2-Y_1)/(X_2-X_1) }}`

`\Rightarrow \displaystyle \mathsf{√((X_2-X_1)^2+(Y_2-Y_1)^2)}}`

`\displaystyle \mathsf{√(\left(-2-\left(-16\right)\right)^2+\left(-18-\left(-15\right)\right)^2)}}`

Solve.

`\displaystyle \mathsf{√(\left(-2+16\right)^2+\left(-18+15\right)^2)}}`

Add & subtract the numbers from left to right.

`\displaystyle \mathsf{(-2+16)^2}}`

`\displaystyle \mathsf{-2+16=14}}`

`\displaystyle \mathsf{14^2}}`

`\displaystyle \mathsf{(-18+15)^2}}`

`\displaystyle \mathsf{-18+15=3}}`

`\displaystyle \mathsf{=3^2}}`

`\displaystyle \mathsf{√(14^2+3^2)}}`

Solve by exponent.

14²=14*14=196

√196+3²

3²=3*3=9

√196+9

Add.

√196+9=205

√205

`\Large\boxed{\mathsf{\Rightarrow √(205)}}}`

So, the correct answer is √205.