Your sock drawer contains ten white socks and ten black socks. If you're only allowed to take one sock from the drawer at a time and you can't see what color sock you're taking until you've taken it, how many socks do you have to take before you're guaranteed to have at least one matching pair?

Warm up Write the equation of the line: Parallel (∥) to 8x – 2y = 6 and goes through (5, -2) in Standard form

Warm up Write the equation of the line: Perpendicular (⊥) to 8x – 2y = 6 and goes through (-5, 3) in Standard form

Given 2 ordered pairs, it’s the AVG of the x’s and AVG of the y’s. Midpoint Given 2 ordered pairs, it’s the AVG of the x’s and AVG of the y’s.

(.5, 5.5) (5.5, 6) Find the midpoint. 1. (3, 7) and (-2, 4)

(8.5, 3.5) (2.5, 13) Find the midpoint. 3. (3, -9) and (14, 16)

Given the midpt and one endpt, find the other endpt. 7. Midpt (3, -6) Endpt (7, -3) (-1, -9)

Given the midpt and one endpt, find the other endpt. 8. Midpt (-1, 2) Endpt (3, 0) (-5, 4)

Given the midpt and one endpt, find the other endpt. 9. Midpt (-4, 6) Endpt (2, 1) (-10, 11)

How to Find the Partition of a Segment Find the Distance between A and B Find the total number of parts (add the ratio or look at the denominator of the fraction) Divide the distance by the number of parts to determine the interval at which each partition will be drawn Draw a partition after the interval found in Step 3 Shade (starting at A) the correct amount of parts (first part of the ratio or the numerator of the fraction) The coordinate of the partition will be wherever you end up

What is a ratio? or A ratio is a comparison of two quantities The ratio of a to b can be expressed as: a : b or a/b or

Connor has a wallet with: 1-$20 bill 2- $10 bills 1- $5 bill 8-$1 bills 1) What is the ratio of $1 bills to $10 bills? 2) What is the ratio of $10 bills to the total number of bills in the wallet?

Point P divides in the ratio 3 to 1. What does this mean?

Where should the knot be tied? A 32 foot long piece of rope has a knot tied to divide the rope into a ratio of 3:5. A B 32 ft Where should the knot be tied?

Example 1: Find the coordinate of point P that lies along the directed line segment from A(3, 4) to B(6, 10) and partitions the segment in the ratio of 3 to 2. Directed Line Segment: Tells the direction in which to start and end. In this case, from Point A to Point B What does that tell you about the distance AP and PB in relation to AB?

Partition – 1 Dimension A is at 1, and B is at 7. Find the point, T, so that T partitions A to B in a 2:1 ratio.

Find the coordinate of point P that lies along the directed line segment from A(3, 4) to B(6, 10) and partitions the segment in the ratio of 3 to 2. Find the rise and run for AB (since you start at A and end at B, make Ax1 and Bx2) (4.8,7.6) 2. Multiply the rise by the ratio from A to P, and the run by the ratio of A to P 3. Add/subtract these values to your starting point A 4. How can you use the distance formula to check that P partitions in the ratio of 3 to 2?

example Find the point Q along the directed line segment from point R(–3, 3) to point S(6, –3) that divides the segment into the ratio 2 to 1 Find the rise and run for RS (since you start at R and end at S, make Rx1 and Sx2) 2. Multiply the rise by the ratio from R to Q, and the run by the ratio of R to Q 3. Add/subtract these values to your starting point R

example Find the point Q along the directed line segment from point R(–2, 4) to point S(18, –6) that divides the segment in the ratio 3 to 7.

example Find the coordinates of the point P that lies along the directed segment from A(1, 1) to B(7, 3) and partitions the segment in the ratio of 1 to 4

Example Find the coordinates of point P that lies along the directed line segment from M to N and partitions the segment in the ratio of 3 to 2