Question

part 3: distance using formula only
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 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 (7)

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

Step3: Solve for (8)

For 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: Solve for (9) a)

Assume from the graph $G(x_1,y_1)$ and $H(x_2,y_2)$ (co - ordinates need to be determined from the graph). Let's say $G(-3,2)$ and $H(2,4)$. Then $d=\sqrt{(2 + 3)^2+(4 - 2)^2}=\sqrt{25+4}=\sqrt{29}\approx5.39$.

Step5: Solve for (9) b)

Assume from the graph $K(x_1,y_1)$ and $L(x_2,y_2)$ (co - ordinates need to be determined from the graph). Let's say $K(6,5)$ and $L(8,1)$. Then $d=\sqrt{(8 - 6)^2+(1 - 5)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\approx4.47$.

Answer:

1. 5
2. 10.05
3. a) Co - ordinates assumed: $G(-3,2),H(2,4)$, Distance $\approx5.39$
4. b) Co - ordinates assumed: $K(6,5),L(8,1)$, Distance $\approx4.47$