Question

1. find the length between c(6, -4) and d(2, -3). 12. the endpoints of $overline{ab}$ are a(-6, 5) and b(-1, -6). find the coordinates of the midpoint, m.

Explanation:

11.

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 6,y_1=-4,x_2 = 2,y_2=-3$.

Step2: Substitute values

$d=\sqrt{(2 - 6)^2+(-3+4)^2}=\sqrt{(-4)^2 + 1^2}=\sqrt{16 + 1}=\sqrt{17}$

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $x_1=-6,y_1 = 5,x_2=-1,y_2=-6$.

Step2: Substitute values

$x=\frac{-6+( - 1)}{2}=\frac{-6 - 1}{2}=-\frac{7}{2}$
$y=\frac{5+( - 6)}{2}=\frac{5 - 6}{2}=-\frac{1}{2}$

Answer:

$\sqrt{17}$

12.