Question

#18: the midpoint of ab is m(2,-3). one endpoint is a(-5,4). what are the coordinates of the other endpoint b? type your answer as an ordered pair in the form (#,#).
9,2

#19: find the distance between x(2,5) and y(13,-5). round to the nearest tenth, if necessary.

Explanation:

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 $A(-5,4)$ be $(x_1,y_1)$ and $B(x,y)$ be $(x_2,y_2)$ and $M(2,-3)$. For the x - coordinate: $\frac{-5 + x}{2}=2$. Cross - multiply: $-5 + x=4$. Then $x = 9$.

Step2: Use mid - point formula for y - coordinate

For the y - coordinate: $\frac{4 + y}{2}=-3$. Cross - multiply: $4 + y=-6$. Then $y=-10$. So the coordinates of $B$ are $(9,-10)$.

Step3: Use distance formula for #19

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, $x_1 = 2,y_1 = 5,x_2 = 13,y_2=-5$.
$d=\sqrt{(13 - 2)^2+(-5 - 5)^2}=\sqrt{11^2+(-10)^2}=\sqrt{121 + 100}=\sqrt{221}\approx14.9$.

Answer:

#18: $(9,-10)$
#19: $14.9$