Day 7 – Finding the Midpoint and Distance in the Coordinate Plane
Finding a Midpoint:
Suppose you have a segment, and you know the coordinates of the endpoints. Can you find the
coordinate that is the midpoint of the segment?
Formula:
y
10
1. Find the coordinates of the midpoint of PQ with endpoints
8
P(–8, 3) and Q(–2, 7).
6
4
2
–10
–8
–6
–4
–2
2
–2
–4
–6
–8
–10
2. Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).
4
6
8
10
x
Day 7 – Finding the Midpoint and Distance in the Coordinate Plane
Finding Distance:
Suppose you have two points in the coordinate plane, and you
connect them to make a segment. What is the distance
between those two points?
y
10
8
6
4
2
–10
–8
–6
–4
–2
2
4
6
8
10
x
–2
–4
–6
–8
Formula:
–10
2. Use the Distance Formula to find the distance from the 2 points below. Round to the nearest
tenth, if necessary.
a. D(3, 4) to E(–2, –5)
b. R(3, 2) and S(–3, –1)
y
10
8
6
4
2
–10
–8
–6
–4
–2
2
4
6
8
10
x
–2
–4
–6
–8
y
–10
10
8
The coordinates of the vertices of ∆ABC are A(2, 5), B(6, –1),
and C(–4, –2). Find the perimeter of ∆ABC, to the nearest
tenth. Show work below.
6
4
2
–10
–8
–6
–4
–2
2
–2
–4
–6
–8
–10
4
6
8
10
x
Day 7 – Finding the Midpoint and Distance in the Coordinate Plane
Using the map of Camp Midway, answer the following…
1. What is the distance from Cabin A (-6, 5) to the lake (-6, -6)?
2. What is the distance from Cabin B (-4, 5) to Cabin C (-2, 5)?
3. What is the distance from Cabin C (-2, 5) to the computer lab (-4, -1)?
4. What is the distance from Cabin C (-2, 5) to the dining hall (2, 8)?
5. Tom left the computer lab (-4, -1) at the same time Jerry left the dining hall (2, 8). If they walked
directly towards each other at the same speed, where did they meet?
6. The campers have traveled between Cabin C (-2, 5), the dining hall (2, 8), and the lodge (5, 6) so
much that they have worn a path in the shape of a triangle. What is the distance around this
path?
7. What is the distance from Cabin A (-6, 5) to the infirmary (3, -3)?
8. The camp Board of Directors is raising funds to build a new dining hall. They plan to place it
midway between the lodge (5, 6) and the infirmary (3, -3). Where will it be located?
9. Joe left Cabin A (-6, 5) and headed 2 units west and 5 units south. At the same time Mike left
Cabin A and headed 1 unit east and 4 units north. Where are they now and how far apart are
they?
10. The Board of Directors has decided to put a fence around the camp. Corners will be at (-6, 10),
(-8, 0), (-8, -8), (4, -6), and (7, 9). How much fencing will be used?