Midpoint and distance in the coordinate plane assignment answer key

Finding the Distance Between Two Points

The logic used to find the distance between two data points on a graph involves the construction of a right triangle using the two data points and the Pythagorean theorem

To do this for the two data points

Using the Pythagorean theorem, this will end up looking like:

or, in expanded form:

On graph paper, this looks like the following. For this illustration, both

The square root of 98 is approximately 9.899 units long.

Find the distance between the points

Start by identifying which are the two data points

Now:

This means that

or

which reduces to

or

Taking the square root, the result is

Finding the Midway Between Two Points (Midpoint)

The logic used to find the midpoint between two data points

In an equation, this looks like:

Find the midpoint between the points

We start by adding the two

or

The midpoint’s

or

The midpoint between the points

Questions

For questions 1 to 8, find the distance between the points.

1.  (−6, −1) and (6, 4)
2. (1, −4) and (5, −1)
3. (−5, −1) and (3, 5)
4. (6, −4) and (12, 4)
5. (−8, −2) and (4, 3)
6. (3, −2) and (7, 1)
7. (−10, −6) and (−2, 0)
8. (8, −2) and (14, 6)

For questions 9 to 16, find the midpoint between the points.

1. (−6, −1) and (6, 5)
2. (1, −4) and (5, −2)
3. (−5, −1) and (3, 5)
4. (6, −4) and (12, 4)
5. (−8, −1) and (6, 7)
6. (1, −6) and (3, −2)
7. (−7, −1) and (3, 9)
8. (2, −2) and (12, 4)

<a class=”internal” href=”/intermediatealgebraberg/back-matter/answer-key-3-2/”>Answer Key 3.2