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Distance, Midpoint, & Slope

Distance, Midpoint, & Slope. d =. d =. d =. The Distance Formula. Find the distance between (-3, 2) and (4, 1). d =. Example:. x 1 = -3, x 2 = 4, y 1 = 2 , y 2 = 1. Exa mple:. Find the distance between (4, -7) and (8, -4). Try :.

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Distance, Midpoint, & Slope

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  1. Distance, Midpoint, &Slope

  2. d = d = d = The Distance Formula Find the distance between (-3, 2) and (4, 1) d = Example: x1 = -3, x2 = 4, y1 = 2 , y2 = 1

  3. Example: Find the distance between (4, -7) and (8, -4)

  4. Try: Find the distance between (-2, 4) and (7, 0)

  5. Try: Find the distance between (-7, 1) and (-4, -1)

  6. Plot the points J, K, L, and M. Draw a segment from J to K and another segment from L to M. Decide if JK and LM are congruent. J (-4, 0) K (4, 8) L (-4, 2) M (3, -7)

  7. Midpoint The ___________________ of a segment is the point that divides the segment into two ___________ segments. A B M

  8. Example: M is the midpoint of . Find the value of x. Then find the measure of EG.

  9. Example Find the lengths of VM, MW, and VW.

  10. M = M = Midpoint Formula Midpoint = Example: Find the midpoint between (-2, 5) and (6, 4) x1= -2, x2= 6, y1 = 5, and y2 = 4

  11. Example: Find the midpoint between (6, -2) and (-4, -5)

  12. Try: Find the midpoint of these two points. • A (4, 2) B ( 1, -3) • 4. R (-3, -2), S (-1, 0) • 5. P(-8, -7), Q( 11, 5)

  13. Finding the missing Endpoint The midpoint of is M (2,1). One endpoint is J (1,4). How do you find the coordinate of K?

  14. Examples: 1. Find endpoint S given that M is the midpoint of RS M (5,3) R (6, -2) S( , ) • Find endpoint S given that M is the midpoint of RS M (-2,0) R (-4, -3) S( , )

  15. Describing Lines • Lines that have a positive slope rise from left to right. • Lines that have a negative slope fall from left to right. • Lines that have no slope (the slope is undefined) are vertical. • Lines that have a slope equal to zero are horizontal.

  16. Slope Definition: The ratio of vertical change (rise) to horizontal change (run) between any two points on the line. Ex: Find the slope of the line containing (-2, 8) and (5, -6). Solution:

  17. Try 1. Find the slope between (3, -5) and (6, 7) and describe it.

  18. m = m = Some More Examples 1. Find the slope between (4, -5) and (3, -5) and describe it. Since the slope is zero, the line must be horizontal. 2. Find the slope between (3,4) and (3,-2) and describe the line. Since the slope is undefined, the line must be vertical.

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