Question

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

Answer 1

Answer:

$\Huge\boxed{\mathsf{\Rightarrow \sqrt{205}}}}$

Step-by-step explanation:

TO FIND:

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

SOLUTIONS:

First, use slope formula.

SLOPE FORMULA:

$\Rightarrow \displaystyle \mathsf{\frac{Y_2-Y_1}{X_2-X_1} }}$

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

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

Solve.

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

Add & subtract the numbers from left to right.

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

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

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

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

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

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

$\displaystyle \mathsf{\sqrt{14^2+3^2}}}$

Solve by exponent.

14²=14*14=196

√196+3²

3²=3*3=9

√196+9

Add.

√196+9=205

√205

$\Large\boxed{\mathsf{\Rightarrow \sqrt{205}}}}$

So, the correct answer is √205.