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1.3 Distance & Midpoint p. 21

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Pythagorean Theorem In a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. (“c” is always the hypotenuse) a b c (leg) (hyp)

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**Distance Formula Where d stands for distance**

x1 & y1 are one endpoint of a segment x2 & y2 are the second endpoint of a segment (x1 , y1) (x2 , y2) d

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**What do you say when you walk into a cold room?**

It’s collinear! (It’s cold in here!)

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Midpoint of a Segment The point halfway between the endpoints of a segment If X is the midpoint of Segment AB , then (the measure of AX = the measure of XB) A B X

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**Midpoint Formula On a Double Number Line (Coordinate Plane):**

On a Single Number Line: x y (5,5) (-3,-1) 5 Units (x1,y1) (x2,y2) A B -3 7 X 2 (1,2)

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(a single number line) M

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(a double number line) (Not to scale) M(2.5, 1.5)

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**Find the Coordinates of an Endpoint**

The Midpoint Formula can be used to find the coordinates of an endpoint when the midpoint and one endpoint are given. Find the coordinates of Endpoint B, if M = 5 is the midpoint, and A = -12 is the other endpoint. 22 17 units (a single number line) A -12 M 5 B ? Multiply both sides by 2 Solve for B

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**(The midpoint is always the ordered pair with no subscripts)**

Let X = (x1,y1) (One endpoint) Y = (-2, 2) (Midpoint) Z = (2, 8) (Other endpoint) (x2, y2) (x, y) (x, y) (x2, y2) (x1, y1) (The midpoint is always the ordered pair with no subscripts) X(?) Y(-2,2) Z(2, 8) (-4, -6)

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**-2x Does it work? +5 Look for an equation to write, then solve:**

Be sure to answer the question.

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Freebies

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HW: Page 25 (3 – 45 odds)

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Benchmark 40 I can find the missing side of a right triangle using the Pythagorean Theorem.

Benchmark 40 I can find the missing side of a right triangle using the Pythagorean Theorem.

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