Section 1-6 Midpoint and Distance in the Coordinate Plane

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Section 1-6 Midpoint and Distance in the Coordinate Plane

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

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

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.

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….

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….

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

Distance Formula

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.

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.

Assignment #

Finding the Distance Using the Pythagorean Theorem

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.

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

Midpoint Formula

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.

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.

Assignment #12