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 $d=\sqrt{(2 - 3)^2+(7+ 3)^2}=\sqrt{(-1)^2+100}=\sqrt{1 + 100}=\sqrt{101}\approx10.05$.

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 $G(-4,1)$ and $H(2,4)$). Then $d=\sqrt{(2 + 4)^2+(4 - 1)^2}=\sqrt{36+9}=\sqrt{45}\approx6.71$.

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 $L(9,1)$). Then $d=\sqrt{(9 - 6)^2+(1 - 5)^2}=\sqrt{9 + 16}=\sqrt{25}=5$.

Answer:

1. 5
2. $\approx10.05$
3. a) $\approx6.71$
4. b) 5