Question

(-15.2, 12.2), (5.8, 4.4)
(a) plot the points.
(b) find the distance between the points.
(c) find the mid - point of the line segment joining the points.

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-15.2,y_1 = 12.2,x_2=5.8,y_2 = 4.4$.

Step2: Calculate differences

$x_2 - x_1=5.8-(-15.2)=5.8 + 15.2=21$ and $y_2 - y_1=4.4 - 12.2=-7.8$.

Step3: Square the differences

$(x_2 - x_1)^2=21^2 = 441$ and $(y_2 - y_1)^2=(-7.8)^2=60.84$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=441+60.84 = 501.84$.

Step5: Calculate the distance

$d=\sqrt{501.84}=22.4$.

Step6: Recall mid - point formula

The mid - point $(x_m,y_m)$ of the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ is given by $x_m=\frac{x_1 + x_2}{2}$ and $y_m=\frac{y_1 + y_2}{2}$.

Step7: Calculate the x - coordinate of the mid - point

$x_m=\frac{-15.2+5.8}{2}=\frac{-9.4}{2}=-4.7$.

Step8: Calculate the y - coordinate of the mid - point

$y_m=\frac{12.2 + 4.4}{2}=\frac{16.6}{2}=8.3$.

Answer:

(b) $22.4$
(c) $(-4.7,8.3)$