Question

kuta software - infinite pre-algebra
name
the distance formula
date 2/9/20
find the distance between each pair of points.
1)
$5^{2}+7^{2}=c^{2}$
2)
3)
4)

Explanation:

Step1: Identify points for Q1

Points: $(-4, -3)$ and $(3, 2)$

Step2: Apply distance formula for Q1

Distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d_1=\sqrt{(3-(-4))^2+(2-(-3))^2}=\sqrt{7^2+5^2}=\sqrt{49+25}=\sqrt{74}$

Step3: Identify points for Q2

Points: $(-2, 2)$ and $(-2, -3)$

Step4: Apply distance formula for Q2

$d_2=\sqrt{(-2-(-2))^2+(-3-2)^2}=\sqrt{0^2+(-5)^2}=\sqrt{25}=5$

Step5: Identify points for Q3

Points: $(0, 0)$ and $(2, -3)$

Step6: Apply distance formula for Q3

$d_3=\sqrt{(2-0)^2+(-3-0)^2}=\sqrt{2^2+(-3)^2}=\sqrt{4+9}=\sqrt{13}$

Step7: Identify points for Q4

Points: $(-5, 3)$ and $(0, -4)$

Step8: Apply distance formula for Q4

$d_4=\sqrt{(0-(-5))^2+(-4-3)^2}=\sqrt{5^2+(-7)^2}=\sqrt{25+49}=\sqrt{74}$

Answer:

1. $\sqrt{74}$
2. $5$
3. $\sqrt{13}$
4. $\sqrt{74}$