1-6 Midpoint & Distance in the Coordinate Plane

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Presentation transcript:

1-6 Midpoint & Distance in the Coordinate Plane Geometry

Geometry Review! What is the difference between the symbols AB and AB? Segment AB The length of Segment AB

The Midpoint Formula The midpoint between the two points (x1,y1) and (x2,y2) is:

Ex. 1)Find the midpoint of the segment whose endpoints are (6,-2) & (2,-9)

Ex. 2 Find the coordinates of the endpoint M is the midpoint of . X has coordinates (2,7) and M has coordinates (6,1). Find the coordinates of Y.

The Distance Formula The Distance d between the points (x1,y1) and (x2,y2) is :

Ex. 3 Find the distance between the two points. (-2,5) and (3,-1) Let (x1,y1) = (-2,5) and (x2,y2) = (3,-1)

Pythagorean Theorem In a right triangle , the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Ex. 4 If A(1,2) & C(1, -3) & D(3,-3), then what is the length of all 3 sides?

Ex. 5 Decide whether the points (6,4), (-3,1), and (9,-5) are vertices of a right triangle. Next, find the sum of the squares of the lengths of the two shorter sides.

Ex. 6 Applying the formulas A grid shows the position of a mall and your house. The mall is located at (1,14) and your house is located at (9,2). a.) What is the distance from your house to the mall? b.) Your friend’s house is at the midpoint of the line between the mall and your house. Where is your friend’s house on the grid?

Assignment