Chapter 1, Problem 10MCQ

To determine

To find the coordinates of the midpoint and then find the distance between each pair

Answer to Problem 10MCQ

Coordinates (-6, -34)

Explanation of Solution

Given information:

M (6, -41) and N (-18, -27)

Formula used:

To calculate coordinate

  $x=\frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}$

To calculate the distance

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

Calculation: calculating the coordinates

Let the coordinates of M (6, -41) be $x_1$ , $y_1$ and N (-18, -27) be $x_2,y_2$

Substituting values in the formula

  $x=\frac{6-18}{2},y=\frac{-41-27}{2}$

Solving it further

  $x=\frac{-12}{2},y=\frac{-68}{2}$

Therefore coordinates are

  $(-6,-34)$

Now, distance between each of the points

First taking M (6, -41) and N (-18, -27)

Substituting values in the formula

Distance = $\sqrt{{\left(-18-6\right)}^2+{\left(-27+41\right)}^2}$

Solving further

  $\sqrt{{\left(-24\right)}^2+{\left(14\right)}^2}=\sqrt{144+49}$

The distance between M and N IS

Distance = $\sqrt{772}=27.8$

Now, take point N (-18, -27) and P (-6, -34)

Substitute values in the formula

Distance = $\sqrt{{\left(-18+6\right)}^2+{\left(-27+34\right)}^2}$

Solving further

Distance = $\sqrt{{\left(-12\right)}^2+{\left(7\right)}^2}$

Solving further

  $\sqrt{144+49}$

Solving further

Distance $=\sqrt{193}=13.8$

Now, take points P (-6, -34) and M (6, -41)

Substitute values in the formula

Distance = $\sqrt{{\left(6+6\right)}^2+{\left(-41+34\right)}^2}$

Solving further

Distance = $\sqrt{{\left(12\right)}^2+{\left(7\right)}^2}$

Solving further

Distance = $\sqrt{144+49}$

Solving further

Distance = $\sqrt{193}=13.8$