Question

for the point p(18, - 12) and q(23, - 9), find the distance d(p,q) and the coordinates of the midpoint m of the segment pq. this test: 15 point(s) possible this question: 1 point(s) possible what is the distance? (simplify your answer. type an exact answer, using radicals as needed.) what are the coordinates of the midpoint m? (simplify your answer. type an ordered pair, using integers or fractions.)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 18,y_1=-12,x_2 = 23,y_2=-9$.

Step2: Calculate the differences

$x_2 - x_1=23 - 18 = 5$ and $y_2 - y_1=-9-(-12)=-9 + 12 = 3$.

Step3: Apply the formula

$d=\sqrt{5^2+3^2}=\sqrt{25 + 9}=\sqrt{34}$.

Step4: Recall mid - point formula

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

Step5: Calculate the mid - point coordinates

$\frac{x_1 + x_2}{2}=\frac{18+23}{2}=\frac{41}{2}$ and $\frac{y_1 + y_2}{2}=\frac{-12+( - 9)}{2}=\frac{-12-9}{2}=-\frac{21}{2}$.

Answer:

What is the distance? $\sqrt{34}$
What are the coordinates of the midpoint M? $(\frac{41}{2},-\frac{21}{2})$