Distance. Essential Question: How do you use the distance formula to find distances and lengths in...
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Transcript of Distance. Essential Question: How do you use the distance formula to find distances and lengths in...
Essential Question: How do you use the distance formula to find distances and
lengths in the coordinate plane?
Distance in the Coordinate Plane
• You can use the Pythagorean Theorem to help you find the Distance between two points.
Distance in the Coordinate Plane
A(2,5) B(-4,-3)
a. Plot the points A and B in the coordinate plane on the right.
b. Draw c. Draw a vertical line through
point Ad. Draw a horizontal line through
point Be. Label the intersection of the
vertical and horizontal line as point C.
Distance in the Coordinate Plane
A(2,5) B(-4,-3)
• Each small square grid square is 1 unit by 1 unit. Use this fact to find the lengths of AC and BC
• AC = _______• BC = _______
Reflect 1b.
• Can you use this method to find the distance between any two points in the coordinate plane? Explain.
The Distance Formula
√(𝑥2−𝑥1)2+(𝑦2−𝑦1)
2
Prove that is longer than
a. Write coordinates: A(___,___)B(___,___)C(___,___)D(___,___)
Reflect 2a.
• When you use the distance formula, does the order in which you subtract the x-coordinates and the y-coordinates matter? Explain.
Essential Question: How do you use the midpoint formula to find the midpoint of a line segment in a coordinate plane?
Midpoints of Line Segments
• Use a ruler: measure the length of the line segment to the nearest millimeter.
• Find half the length of the segment.
Reflect 1a.
• Make a conjecture: If you know the coordinates of the endpoints of a line segment, how can you find the coordinates of the midpoint?
Reflect 1b.
• What are the coordinates of the midpoint of a line segment with endpoints at the origin and at the point ?
The Midpoint Formula
𝑀 ( 𝒙𝟏+𝒙𝟐
𝟐,𝒚𝟏+𝒚𝟐
𝟐 )has endpoints and Prove that the midpoint of lies in Quadrant III.
Identify : _______: _______: _______: _____