Chapter 1, Problem 7MCQ

To determine

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

Answer to Problem 7MCQ

Midpoints R (1, -1)

Distance between

PQ = 7.07

PR = 3.60

QR = 3.60

Explanation of Solution

Given information:

P (4, 1) and Q (-2, -3)

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 (4, 1) be $x_1$ , $y_1$ and Q (-2, -3) be $x_2,y_2$

Substituting values in the formula

  $x=\frac{4-2}{2},y=\frac{1-3}{2}$

Solving it further

  $x=\frac{2}{2},y=-\frac{2}{2}$

The coordinates are

  $x=1,y=-1$

R (1, -1)

Now find distance between each points

First take P (4, 1) and Q (2, -3)

Substitute value in the formula

Distance = $\sqrt{{\left(-2-4\right)}^2+{\left(-3-1\right)}^2}$

Solving further

Distance = $\sqrt{{\left(-6\right)}^2+{\left(-4\right)}^2}$

Solving further

Distance = $\sqrt{36+16}$

Distance is

Distance = $\sqrt{52}=7.07$

Now take P (4, 1) And R (1, -1)

Substitute values in the formula

Distance = $\sqrt{{\left(1-4\right)}^2+{\left(-1-1\right)}^2}$

Solving further

Distance = $\sqrt{{\left(-3\right)}^2+{\left(-2\right)}^2}$

Solving further

  $\sqrt{9+4}$

Solving further

  $\sqrt{13}=3.60$

Now, take Q (-2, -3) and R (1, -1)

Substitute values in the formula

Distance = $\sqrt{{\left(-2-1\right)}^2+{\left(-3+1\right)}^2}$

Solving further

  $\sqrt{{\left(-3\right)}^2+{\left(-2\right)}^2}$

Solving further

  $\sqrt{9+4}$

Solving further

  $\sqrt{13}=3.60$