Question

Find the distance between points P(7, 4) and Q(1, 2) to the nearest tenth.
What is the midpoint of
PQ?

Answer 1

the distance between the points are -17

Answer 2

The distance between points PQ is $2\sqrt{10}$.

The midpoint of PQ is $( 4, 3)$.

Given that,

The points are P(7, 4) and Q(1, 2).

We have to determine,

The distance between the points and,

The midpoint of PQ.

According to the question,

To calculate the distance between two points by using distance formula;

$Distance \ formula = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 }$

Where,  $x_1 = 7 , y_1 = 4 , x_2 = 1 , y_2 = 2$

Substitute the values in the formula;

$PQ = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 }\\\\PQ = \sqrt{(1-7)^2 + (2-4)^2 }\\\\PQ = \sqrt{(-6)^2 + (-2)^2 }\\\\PQ = \sqrt{36+ 4 }\\\\PQ = \sqrt{40}\\\\PQ = 2\sqrt{10}$

And, The midpoint of PQ calculated by using formula;

$Midpoint \ of \ PQ = (\dfrac{x_1+x_2}{2} , \dfrac{y_1+y_2}{2} )$

Where,  $x_1 = 7 , y_1 = 4 , x_2 = 1 , y_2 = 2$

Substitute the values in the formula;

$Midpoint \ of \ PQ = (\dfrac{7+1}{2} ,\dfrac{4+2}{2} )\\\\Midpoint \ of \ PQ = (\dfrac{8}{2} ,\dfrac{6}{2} )\\\\Midpoint \ of \ PQ = (4,3)$

Hence, The distance between points PQ is $2\sqrt{10}$.

The midpoint of PQ is $( 4, 3)$.

To know more about Distance Formula click the link given below.

https://brainly.com/question/12344210