Question

find the distance between the two points. round your answer to the nearest tenth.

1. a(2.5, 3.5), b(-4, 0.5) 15. a\\(\left(-1\frac{1}{2}, 2\

ight)\\), b\\(\left(3, -1\frac{1}{2}\
ight)\\)

Explanation:

Problem 14:

Step1: Recall distance formula

The distance $d$ between points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Substitute values $A(2.5,3.5), B(-4,0.5)$

$d=\sqrt{(-4-2.5)^2+(0.5-3.5)^2}$

Step3: Calculate differences

$d=\sqrt{(-6.5)^2+(-3)^2}$

Step4: Compute squares

$d=\sqrt{42.25+9}$

Step5: Sum and take square root

$d=\sqrt{51.25}\approx7.2$

Problem 15:

Step1: Convert mixed numbers to decimals

$A(-1\frac{1}{2},2)=(-1.5,2)$, $B(3,-1\frac{1}{2})=(3,-1.5)$

Step2: Substitute into distance formula

$d=\sqrt{(3-(-1.5))^2+(-1.5-2)^2}$

Step3: Calculate differences

$d=\sqrt{(4.5)^2+(-3.5)^2}$

Step4: Compute squares

$d=\sqrt{20.25+12.25}$

Step5: Sum and take square root

$d=\sqrt{32.5}\approx5.7$

Answer:

1. $7.2$
2. $5.7$