1. Section 1-6 Midpoint and Distance in the Coordinate Plane

2. Perfect Squares 64
225 1 81
400 4
100
625 9
121 16
144 25
169 36
196 49

3. What is a square root?
A square root, is a number, when multiplied by itself, forms a perfect square.

4. Estimating Square roots
Sometimes, the number inside the radical is not a perfect square. So how do we find the square root?
We need to estimate…
Step 1: Decide which two integers the square root is in between.
Step 2: Now estimate, to the nearest tenth.

5. Example 1 Find the square root The two closest perfect squares are:
So, my solution must be between 2 and 3.
Since 7 is a little more than halfway between 4 and 9….

6. Example 2 Find the square root The two closest perfect squares are:
So, my solution must be between 3 and 4.
Since 15 is very close to 16….

7. Parts of the Coordinate Plane
Y axis
Quadrant II
Quadrant I
(-,+)
(+,+)
origin
X axis
Quadrant III
Quadrant IV
(-,-)
(+,-)

8. Distance Formula

9. Example 3
Find the distance between (3,-4) and (6,0). If necessary, round your answer to the nearest tenth.
Step 1: Label the given points:
Step 2: Plug the variables into the distance formula
Step 3: Simplify.
Step 4: If necessary, round to the nearest tenth.

10. Example 4 Find the distance between the points: (-1,-2) and (2,4)
Step 1: Label the given points:
Step 2: Plug the variables into the distance formula
Step 3: Simplify.
Step 4: If necessary, round to the nearest tenth.

11. Assignment #

12. Finding the Distance Using the Pythagorean Theorem

13. Finding the Distance Using the Pythagorean Theorem
Step 1: Graph the given points. Sketch a right triangle.
Step 2: Count the units for each of the smaller sides. This will be your a and b.
Step 3: Plug in a and b and solve for c to find the distance.

14. Example 5
Use the Pythagorean Theorem to find the distance between: (-2,3) and (2,-2). If necessary, round to the nearest tenth. 4 5

15. Midpoint Formula

16. Example 6 Find the midpoint between (-2, 5) and (6, 3)
Step 1: Label the points
Step 2: Plug the variables into the midpoint formula
Step 3: Simplify.
Step 4: Write your solution as an ordered pair.

17. Finding the Coordinates of an Endpoint Example 7
M is the midpoint of segment AB. A has coordinates (2,2), and M has coordinates (4, -3). Find the coordinates of B.

18. Assignment #12