Lesson 1-3: Use Distance and Midpoint Formulas

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Presentation transcript:

Lesson 1-3: Use Distance and Midpoint Formulas

Midpoints and Bisectors: The midpoint of a segment is the point that divides the segment into two congruent segments. A segment bisector is a point, ray, line, line segment, or plane that intersects the segment at its midpoint.

In the skateboard design, bisects at point T, and XT = 39. 9 cm In the skateboard design, bisects at point T, and XT = 39.9 cm. Find XY.

Line n bisects the segment. Find the indicated length. Find DF if EF= 9 ½ m B A C Find AB if BC = 5/8 cm

n B A C Find AB if AC = 21 inches

Point M is the midpoint of . Find the length of .

Identify the segment bisector of . Then find PQ. 14

w M A C x + 20 5x - 4 Find AC

The Midpoint Formula: If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the midpoint M of has coordinates Midpoint (M) =

Ex: The endpoints of RS are R(1, -3) and S(4, 2) Ex: The endpoints of RS are R(1, -3) and S(4, 2). Find the coordinates of the midpoint M. Ex: The endpoints of GH are G(7, -2) and H(-5, -6). Find the coordinates of the midpoint P.

Ex: The midpoint of JK is M(2, 1). One endpoint is J(1, 4) Ex: The midpoint of JK is M(2, 1). One endpoint is J(1, 4). Find the coordinates of endpoint K.

Ex: The midpoint of AB is M(5, 8). One endpoint is A(2, -3) Ex: The midpoint of AB is M(5, 8). One endpoint is A(2, -3). Find the coordinates of endpoint B.

Ex: The midpoint of AB is M(3, -4). One endpoint is A(-4, -6) Ex: The midpoint of AB is M(3, -4). One endpoint is A(-4, -6). Find the coordinates of endpoint B.

Distance Formula: To find the distance between two points, you will always use the Distance Formula. The Distance Formula: If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the distance between A and B is distance (d) =

Ex: What is the approximate length of RS with endpoints R(2, 3) and S(4, -1)? Round to the nearest tenth of a unit.

Ex: What is the approximate length of AB with endpoints A(-3, 2) and B(1, -4)? Round to the nearest tenth of a unit.

Find the length of the segment. Round to the nearest tenth of a unit.

The endpoints of two segments are given. Find each segment length The endpoints of two segments are given. Find each segment length. Tell whether the segments are congruent. AB: A(-4, 0), K(4,8) CD: C(-4, 2), D(3, -7)

Homework! Pgs 19-21 #1, 3-20 all, 26-34 even, 43-45, 48, 49