Question

For the point Pleft parenthesis 5 comma 2 right parenthesis and Qleft parenthesis 12 comma 7 right parenthesis​, find the distance​ d(P,Q) and the coordinates of the midpoint M of the segment PQ.

Answer 1

Answer:

The distance is $\sqrt{74}$ which is approximately equal to 8.602 units

The midpoint is (8.5 , 5.5)

Explanation:

1- Getting the distance:

The distance between two points can be calculated using the following rule:

$Distance = \sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}$

The given points are:

(5,2) represents (x₁ , y₁)

(12,7) represents (x₂ , y₂)

Substitute with the givens in the above equation to get the distance as follows:

$Distance = \sqrt{(12-5)^2+(7-2)^2}=\sqrt{74} = 8.602 units$

2- Getting the midpoint:

The midpoint of two points is calculated as follows:

$Midpoint = (\frac{x_{1}+x_{2}}{2} , \frac{y_{1}+y_{2}}{2})$

The given points are:

(5,2) represents (x₁ , y₁)

(12,7) represents (x₂ , y₂)

Substitute with the givens in the above equation to get the distance as follows:

$Midpoint = (\frac{5+12}{2} , \frac{2+7}{2}) = (8.5 , 4.5)$

Hope this helps :)