Question

graph the points and find the distance between each set of points. when necessary, round to the nearest tenth.

1. (0, -3) and (3, 4)
2. (-2, 1) and (6, -5)

Explanation:

Step1: Recall distance formula

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

---

For problem 6: $(0,-3)$ and $(3,4)$

Step2: Assign values to variables

Let $(x_1,y_1)=(0,-3)$, $(x_2,y_2)=(3,4)$

Step3: Compute coordinate differences

$x_2-x_1=3-0=3$, $y_2-y_1=4-(-3)=7$

Step4: Substitute into distance formula

$d=\sqrt{3^2+7^2}=\sqrt{9+49}=\sqrt{58}$

Step5: Calculate decimal value

$\sqrt{58}\approx7.6$

---

For problem 7: $(-2,1)$ and $(6,-5)$

Step2: Assign values to variables

Let $(x_1,y_1)=(-2,1)$, $(x_2,y_2)=(6,-5)$

Step3: Compute coordinate differences

$x_2-x_1=6-(-2)=8$, $y_2-y_1=-5-1=-6$

Step4: Substitute into distance formula

$d=\sqrt{8^2+(-6)^2}=\sqrt{64+36}=\sqrt{100}$

Step5: Simplify the square root

$\sqrt{100}=10$

Answer:

1. Distance between $(0,-3)$ and $(3,4)$: $\approx7.6$
2. Distance between $(-2,1)$ and $(6,-5)$: $10$