Question

find the distance between the two points (2, 8) and (3, -2)
√71
√37
√101
√41
10 multiple choice 1 point
find the midpoint of the line segment joining the two points (3, -2) and (-1, 7).
(-1, 5)
(2, 5)
(2, 9/2)
(1, 5/2)

Explanation:

Step1: Recall distance formula

The distance $d$ 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, $(x_1,y_1)=(2,8)$ and $(x_2,y_2)=(3, - 2)$.

Step2: Substitute values

$d=\sqrt{(3 - 2)^2+(-2 - 8)^2}=\sqrt{1^2+(-10)^2}=\sqrt{1 + 100}=\sqrt{101}$

Step3: Recall mid - point formula

The mid - point $M$ of the line segment joining 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, $(x_1,y_1)=(3,-2)$ and $(x_2,y_2)=(-1,7)$.

Step4: Substitute values for mid - point

$x=\frac{3+( - 1)}{2}=\frac{2}{2}=1$ and $y=\frac{-2 + 7}{2}=\frac{5}{2}$. So the mid - point is $(1,\frac{5}{2})$.

Answer:

1. C. $\sqrt{101}$
2. D. $(1,\frac{5}{2})$