Question

what the length of 11 and 12?

1. a(6, 8), b(-1, 8)
2. c(5, -6), d(5, 6)

Explanation:

Step1: Recall distance formula for two - points

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 for 11

For points $A(6,8)$ and $B(-1,8)$, $x_1 = 6,y_1 = 8,x_2=-1,y_2 = 8$. Substitute into the formula:
$d_{AB}=\sqrt{(-1 - 6)^2+(8 - 8)^2}=\sqrt{(-7)^2+0^2}=\sqrt{49}=7$.

Step3: Calculate distance for 12

For points $C(5,-6)$ and $D(5,6)$, $x_1 = 5,y_1=-6,x_2 = 5,y_2 = 6$. Substitute into the formula:
$d_{CD}=\sqrt{(5 - 5)^2+(6-(-6))^2}=\sqrt{0+(6 + 6)^2}=\sqrt{12^2}=12$.

Answer:

1. 7
2. 12