distance and midpoints. you are vacationing in an unfamiliar place. you ask the clerk in the hotel...
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Essential Questions When does distance make a difference in life? Can distance ever be negative?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
2 22 1 2 1( ) ( )d x x y y
The distance between any two points with coordinates and
is given by the formula1 1( , )x y 2 2( , )x y
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.
SmallLeg2 + LargeLeg22 = Hypontenuse2
Example 2Find the distance from H(2,3) to K(-3,-1) by using the Pythagorean Theorem.
Just beyond Midway, PA
Midpoint FormulaMidpoint—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.