Question

find the distance between each set of points (round to 2 dp if needed, no graphing needed). show the formula and all work.

1. (0, 0) and (4, 3)
2. (3, - 3) and (2, 7)
3. determine the coordinates of the points needed. then find the distance of each line - segment (round to 2 dp):

a) gh g( , ) h( , )
b) kl k( , )

Explanation:

Step1: Recall the distance formula

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

Step2: Solve for the points $(0,0)$ and $(4,3)$

Let $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(4,3)$. Then $d=\sqrt{(4 - 0)^2+(3 - 0)^2}=\sqrt{4^2+3^2}=\sqrt{16 + 9}=\sqrt{25}=5$.

Step3: Solve for the points $(3,-3)$ and $(2,7)$

Let $(x_1,y_1)=(3,-3)$ and $(x_2,y_2)=(2,7)$. Then $d=\sqrt{(2 - 3)^2+(7+ 3)^2}=\sqrt{(-1)^2+10^2}=\sqrt{1 + 100}=\sqrt{101}\approx10.05$.

Step4: Determine coordinates for segment $GH$ from the graph

Assume from the graph $G(-3,1)$ and $H(2,4)$. Then $d=\sqrt{(2 + 3)^2+(4 - 1)^2}=\sqrt{5^2+3^2}=\sqrt{25+9}=\sqrt{34}\approx5.83$.

Step5: Determine coordinates for segment $KL$ from the graph

Assume from the graph $K(5,5)$ and $L(7,-2)$. Then $d=\sqrt{(7 - 5)^2+(-2 - 5)^2}=\sqrt{2^2+(-7)^2}=\sqrt{4 + 49}=\sqrt{53}\approx7.28$.

Answer:

1. $5$
2. $\approx10.05$
3. a) $G(-3,1),H(2,4),d\approx5.83$

b) $K(5,5),L(7,-2),d\approx7.28$