Question

for the points (29.8, -5.7) and (23.8, -13.7), (a) find the exact distance between the points. (b) find the midpoint of the line segment whose endpoints are the given points. part 1 of 2 (a) the exact distance between the points is \boxed{\sqrt{\square}}. part 2 of 2 (b) the midpoint is \boxed{(\square,\square)}. (write your answer in decimal form.)

Explanation:

Step1: Assign points to variables

Let $(x_1,y_1)=(29.8, -5.7)$ and $(x_2,y_2)=(23.8, -13.7)$

Step2: Calculate distance using formula

Distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$$\begin{align*} d&=\sqrt{(23.8-29.8)^2+(-13.7-(-5.7))^2}\\ &=\sqrt{(-6)^2+(-8)^2}\\ &=\sqrt{36+64}\\ &=\sqrt{100} \end{align*}$$

Step3: Simplify distance value

$d=10$

Step4: Calculate midpoint x-coordinate

Midpoint x: $\frac{x_1+x_2}{2}=\frac{29.8+23.8}{2}=\frac{53.6}{2}=26.8$

Step5: Calculate midpoint y-coordinate

Midpoint y: $\frac{y_1+y_2}{2}=\frac{-5.7+(-13.7)}{2}=\frac{-19.4}{2}=-9.7$

Answer:

(a) $10$
(b) $(26.8, -9.7)$