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

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Presentation transcript:

Distance, Midpoint, & Slope

The Distance Formula Find the distance between (-3, 2) and (4, 1) x 1 = -3, x 2 = 4, y 1 = 2, y 2 = 1 d = Example:

Find the distance between (4, -7) and (8, -4)

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

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

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)

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

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

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

Midpoint Formula M = Find the midpoint between (-2, 5) and (6, 4) x 1 = -2, x 2 = 6, y 1 = 5, and y 2 = 4 Example: Midpoint =

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

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

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?

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

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.

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:

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

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. m = 2. Find the slope between (3,4) and (3,-2) and describe the line. m = Since the slope is undefined, the line must be vertical.