Distance and Midpoints. You are vacationing in an unfamiliar place. You ask the clerk in the hotel lobby where the nearest coffee shop is, within walking.

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Presentation transcript:

Distance and Midpoints

You are vacationing in an unfamiliar place. You ask the clerk in the hotel lobby where the nearest coffee shop is, within walking distance. one block? 2 or 3 blocks? An hour on foot? Is “walking distance” a universally understood term? Is it an accurate measure? What is walking distance? A mile or two?

Essential Questions When does distance make a difference in life? Can distance ever be negative?

Coordinate Plane Graph the following points: point A (1,3) point B (-2,4) point C (-4, -3) point D (2,-5)

Distance on a number line What is PQ if a=1, b=5? What if a=-10, b=3?

Distance Formula The distance between any two points with coordinates and is given by the formula

Essential Questions Can distance ever be negative? Why or why not?

Example 1 Find the distance from A(-4,-3) to B(2, 5) using the Distance Formula.

Pythagorean Theorem In a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse. SmallLeg 2 + LargeLeg2 2 = Hypontenuse 2

Example 2 Find the distance from H(2,3) to K(-3,-1) by using the Pythagorean Theorem.

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Midpoint Formula Midpoint—the point halfway between the endpoints of a segment

Examples The coordinates on a number line of J and K are -12 and 16 find the midpoint of line segment JK Point G has the coordinate (8, -6), the midpoint has the coordinate (-3, 3) find the coordinate of the end of the line segment.