Question

1. eb is a segment and m is the mid - point of segment eb. e(11, - 4) m(6, 2) find the coordinate of the endpoint b. a) b(17,2) b) b(9,2) c) b(8, - 6) d) b(1,8) 9) use the distance formula to find the distance between a(10,9) and c(22,4) a) d = 44 b) d = 13 c) d = 25 d) d = 38 10) bonus m is between c an g. if cm = 2x, mg = x + 6, and cg = 48, then what is the equation for solving x? a) 2x = x + 6 b) 2x = 48 c) 2x + x + 6 = 48 d) 2x - x + 6 = 48

Explanation:

8.

Step1: Use mid - point formula for x - coordinate

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $E(x_1,y_1)=(11,-4)$ and $M(x_m,y_m)=(6,2)$ and $B(x_2,y_2)$. For the x - coordinate, $\frac{x_1 + x_2}{2}=x_m$. Substitute the values: $\frac{11 + x_2}{2}=6$. Solving for $x_2$ gives $11+x_2 = 12$, so $x_2=1$.

Step2: Use mid - point formula for y - coordinate

For the y - coordinate, $\frac{y_1 + y_2}{2}=y_m$. Substitute $y_1=-4$ and $y_m = 2$: $\frac{-4 + y_2}{2}=2$. Then $-4 + y_2=4$, so $y_2 = 8$.

Step1: Recall the 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, $x_1 = 10,y_1 = 9,x_2=22,y_2 = 4$.

Step2: Substitute values into the formula

$d=\sqrt{(22 - 10)^2+(4 - 9)^2}=\sqrt{12^2+( - 5)^2}=\sqrt{144 + 25}=\sqrt{169}=13$.

Step1: Use the segment - addition postulate

Since $M$ is between $C$ and $G$, by the segment - addition postulate, $CM+MG=CG$. Given $CM = 2x$, $MG=x + 6$ and $CG = 48$, we substitute these values into the equation.

Answer:

D. B(1,8)

9.