Question

find the mid - point of the line segment whose end points are given. (4, 3/2) and (1, - 2)
(13/10, 3/4)
(1/10, - 3/4)
(9/10, 1/4)
(9/10, 3/4)
question 8
find the distance between the pair of points. (6, - 1) and (4, - 7)
4
12√2
32
2√10

Explanation:

Step1: Recall distance formula

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

Step2: Identify coordinates

Here, $(x_1,y_1)=(6,-1)$ and $(x_2,y_2)=(4,-7)$.

Step3: Substitute values

$d=\sqrt{(4 - 6)^2+((-7)-(-1))^2}=\sqrt{(-2)^2+(-6)^2}$.

Step4: Calculate squares

$\sqrt{(-2)^2+(-6)^2}=\sqrt{4 + 36}=\sqrt{40}$.

Step5: Simplify square - root

$\sqrt{40}=\sqrt{4\times10}=2\sqrt{10}$.

Answer:

$2\sqrt{10}$