Chapter 1, Problem 9MCQ

To determine

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

Answer to Problem 9MCQ

Midpoints (17, 27)

Distance between

PQ = 35

PR = 17

QR = 17

Explanation of Solution

Given information:

P (26, 12) and Q (8, 42)

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 P (26, 12) be $x_1$ , $y_1$ and Q (8, 42) be $x_2,y_2$

Substituting values in the formula

  $x=\frac{26+2}{2},y=\frac{12+42}{2}$

Solving it further

  $x=\frac{28}{2},y=\frac{54}{2}$

The coordinates are

  $x=14,y=27$ (14, 27)

Now find distance between each points

First take P (26, 12) and Q (8, 42)

Substitute value in the formula

Distance = $\sqrt{{\left(8-26\right)}^2+{\left(42-12\right)}^2}$

Solving further

Distance = $\sqrt{{\left(-18\right)}^2+{\left(30\right)}^2}$

Solving further

Distance = $\sqrt{324+900}$

Distance is

Distance = $\sqrt{1224}=34.9or35$

Now take P (26, 12) And R (17, 27)

Substitute values in the formula

Distance = $\sqrt{{\left(17-26\right)}^2+{\left(27-12\right)}^2}$

Solving further

Distance = $\sqrt{{\left(-9\right)}^2+{\left(15\right)}^2}$

Solving further

  $\sqrt{81+225}$

Solving further

  $\sqrt{306}=17.49or17$

Now, take Q (8, 42) and R (17, 27)

Substitute values in the formula

Distance = $\sqrt{{\left(17-8\right)}^2+{\left(27-42\right)}^2}$

Solving further

  $\sqrt{{\left(9\right)}^2+{\left(15\right)}^2}$

Solving further

  $\sqrt{81+225}$

Solving further

  $\sqrt{306}=17.49or17$