Question

What is the length of the segment that joins the points: (-2, 3) and (-8, -7)?

Write your answer in simplified radical form

Answer 1

\(\bf \large \color{red}{The ~Distance ~Formula}\)

The distance, d, between points \((x_1, y_1)\) and \((x_2, y_2) \) is

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Choose one point to be \((x_1, y_1)\) and the other point to be \((x_2, y_2) \) and substitute the coordinates in the formula to find d.

Answer 2

Is the answer square root of 136?

Answer 3

Let's try it:

\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

\(d = \sqrt{(-8 - (-2))^2 + (-7 - 3)^2}\)

\(d = \sqrt{(-6)^2 + (-10)^2}\)

\(d = \sqrt{36 + 100}\)

\(d = \sqrt{136}\)

You are correct, it is \( \sqrt{136} \).
Now we need to see if we can simplify the radical.

Answer 4

Does 136 have a perfect-square factor?

Answer 5

34 square root 2?

Answer 6

\(\sqrt{136} = \sqrt{4 \times 34} = 2\sqrt{34}\)

Answer 7

Sorry, please notice the correct answer.
The 34 stays in the square root.
The square root of 4 comes out as 2.

Answer 8

Thank you! and while youre here can you tell me if I got this other question right?
the question was: What is the midpoint of the segment that joins the endpoints (-3, 12) and (-7, -20)?
I got (-5, -4)

Answer 9

Correct. There all you need to do is average the two x-coordinates and average the two y-coordinates which you did correctly.

x-coordinate: (-3 + (-7))/2 = -10/2 = -5
y-coordinate: (12 + (-20))/2 = -8/2 = -4

Answer: (-5, -4), exactly what you got.
Great job!

Answer 10

Thank you! I have two other questions I am unsure of that I will post. Thanks again!!