Question

topic 1 using a rectangular coordinate system skills practice continued
3 a (5, 8), b (5, 2), c (-3, 5)
4 a (-2, -6), b (6, -6), c (2, -3)
5 a (0, 0), b (4, 0), c (3, 7)
6 a (-6, 4), b (0)

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: Calculate distance $AB$ for points $A(5,8)$ and $B(5,2)$

Here $x_1 = 5,y_1 = 8,x_2 = 5,y_2 = 2$. Substitute into the formula:
$AB=\sqrt{(5 - 5)^2+(2 - 8)^2}=\sqrt{0+( - 6)^2}=\sqrt{36}=6$.

Step3: Calculate distance $BC$ for points $B(5,2)$ and $C(-3,5)$

Here $x_1 = 5,y_1 = 2,x_2=-3,y_2 = 5$. Then $BC=\sqrt{(-3 - 5)^2+(5 - 2)^2}=\sqrt{(-8)^2+3^2}=\sqrt{64 + 9}=\sqrt{73}$.

Step4: Calculate distance $CA$ for points $C(-3,5)$ and $A(5,8)$

Here $x_1=-3,y_1 = 5,x_2 = 5,y_2 = 8$. So $CA=\sqrt{(5+3)^2+(8 - 5)^2}=\sqrt{8^2+3^2}=\sqrt{64+9}=\sqrt{73}$.

Answer:

$AB = 6$, $BC=\sqrt{73}$, $CA=\sqrt{73}$