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## Pythagorean Theorem, Distance Formula and Midpoint Formula

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**Pythagorean Theorem Word Problems**• A square has a diagonal with length of 20 cm. What is the measure of each side? Round to the nearest tenths.**Pythagorean Theorem Word Problems**• A 25 foot ladder is leaning against a building. The foot of the ladder is 15 feet from the base of the building. How high is the top of the ladder along the building? Round to the nearest tenths.**Pythagorean Theorem Word Problems**• Ashley travels 42 miles east, then 19 miles south. How far is Ashley from the starting point? Round to the nearest tenths.**Pythagorean Theorem Word Problems**• What is the length of the altitude of an equilateral triangle if a side is 12 cm? Round to the nearest tenths.**The Distance Formula**Given two points:**Example**Find the distance between (1, 4) and (-2, 3). Round to the nearest hundredths. D 3.16**Example**Find the distance between the points, (10, 5) and (40, 45). Round to the nearest hundredths. D = 50**3. Find the distance between the points. Round to the**nearest tenths. 3.6**4. Find the distance between the points. Round to the**nearest tenths. 3.2**Midpoint**Given 2 ordered pairs, it’s the AVG of the x’s and AVG of the y’s.**Find the midpoint.**1. (3, 7) and (-2, 4) 2. (5, -2) and (6, 14) (.5, 5.5) (5.5, 6)**Find the midpoint.**3. (3, -9) and (14, 16) 4. (12, 17) and (-7, 9) (8.5, 3.5) (2.5, 13)**Find the midpoint.**5. (2, 3)**Find the midpoint.**6. (1.5, 4)**Given the midpt and one endpt, find the other endpt.**7. Midpt(3, -6) Endpt(7, -3) (-1, -9)**Given the midpt and one endpt, find the other endpt.**8. Midpt(-1, 2) Endpt(3, 0) (-5, 4)**Given the midpt and one endpt, find the other endpt.**9. Midpt(-4, 6) Endpt(2, 1) (-10, 11)