Section 1.7 Midpoint and Distance in the Coordinate Plane 1.7 Distance and Midpoint Objective: Students will be able to: find the midpoint of a segment find the distance between two points in the coordinate plane 1.7 Distance and Midpoint
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Presentation Transcript
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Section 1.7 Midpoint and Distance in the Coordinate Plane 1.7 Distance and Midpoint<br>
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Objective: Students will be able to:
find the midpoint of a segment
find the distance between two points in the coordinate plane 1.7 Distance and Midpoint<br>
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Vocabulary: Midpoint
Distance
Bisect 1.7 Distance and Midpoint<br>
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Vocabulary: What do you think we mean
by the word “midpoint”?
Ideas on how to find it on a number line?
Ideas on how to find it on a coordinate plane? 1.7 Distance and Midpoint<br>
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You can use formulas to find the midpoint and length of any segment in the coordinate plane. 1.7 Distance and Midpoint<br>
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Problem 1:
Segment AB has endpoints at -4 and 9. What is the coordinate of its midpoint?
Segment JK has endpoints at -12 and 4 on a number line. What is the coordinate of its midpoint? 1.7 Distance and Midpoint<br>
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Problem 1 Solution:
Segment AB has endpoints at -4 and 9. What is the coordinate of its midpoint? A B - 4 9 Using the midpoint formula we have: ? 1.7 Distance and Midpoint<br>
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Problem 1 Solution: Segment JK has endpoints at -12 and 4 on a number line. What is the coordinate of its midpoint? J K - 12 4 Using the midpoint formula we have: ? 1.7 Distance and Midpoint<br>
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Problem 1b:
Segment EF has endpoints E(7, 5) and
F(2, -4). What are the coordinates of its midpoint M?
Segment RS has endpoints at R(5, -10) and S(3, 6). What are the coordinates of its midpoint M? 1.7 Distance and Midpoint<br>
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Problem 1b:
Segment EF has endpoints E(7, 5) and
F(2, -4). What are the coordinates of its midpoint M? We use the same concept. Use the midpoint formula to the x and to the y coordinates and we have: Midpoint: 1.7 Distance and Midpoint<br>
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Problem 1b Solution:
Segment RS has endpoints at R(5, -10) and S(3, 6). What are the coordinates of its midpoint M? We use the same concept. Use the midpoint formula to the x and to the y coordinates and we have: Midpoint: 1.7 Distance and Midpoint<br>
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Problem 2 Solution:
The midpoint of Segment CD is M(2, -1). One endpoint is C(-5, 7). What are the coordinates of the other endpoint D?
The midpoint of Segment AB is M(4, -9). One endpoint is A(-3, -5). What are the coordinates of the other endpoint B? 1.7 Distance and Midpoint<br>
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Problem 2 Solution:
The midpoint of Segment CD is M(2, -1). One endpoint is C(-5, 7). What are the coordinates of the other endpoint D? NOTICE: Here we are looking for the END, not the midpoint. The midpoint is given. D: C D (2, -1) (-5, 7) ? 1.7 Distance and Midpoint<br>
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Problem 2 Solution:
The midpoint of Segment AB is M(4, -9). One endpoint is A(-3, -5). What are the coordinates of the other endpoint B? NOTICE: Here we are looking for the END, not the midpoint. The midpoint is given. B: A B (4, -9) (-3, -5) ? 1.7 Distance and Midpoint<br>
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To find the distance between any two points in a coordinate plane, you can use the Distance Formula.
Do you remember any other way to find the distance between to coordinate points in a plane? 1.7 Distance and Midpoint<br>
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Problem 3:
What is the distance between U(-7, 5) and V(4, -3)? Round to the nearest tenth. 1.7 Distance and Midpoint<br>
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Problem 3 Solution:
What is the distance between U(-7, 5) and V(4, -3)? Round to the nearest tenth. 1.7 Distance and Midpoint<br>
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Problem 3 Solution:
Segment SR has endpoints S(-2, 14) and
R(3, -1). What is SR to the nearest tenth? 1.7 Distance and Midpoint<br>
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Problem 3 Solution:
Segment SR has endpoints S(-2, 14) and
R(3, -1). What is SR to the nearest tenth? 1.7 Distance and Midpoint<br>