Warm-up: 1. Find the equation of the line parallel to y = 3x – 1 that goes through the point (-3, -5). 2. Find the equation of the line perpendicular to a line that goes through the points (4, 3) and (3, -1) and passes through (-3, 3).

Segment ratio (Partitioning segment) Unit 11 Notes…

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

Let’s practice  Drew has a wallet with 1 $20 bill, 2 $10 bills, 1 $5 bill, and 8 $1 bills. What is the ratio of $1 bills to $10 bills? What is the ratio of $10 bills to the total number of bills in his wallet?

Segment ratio Point P divides 𝑨𝑩 in the ratio 3 to 1. What does this mean? Do you expect point P to be closer to A or closer to B? Why? How does the slope of 𝐴𝑃 compare with the slope of 𝐴𝐵 ? Why?

Think about it! A 32 foot long piece of rope has a knot tied to divide the rope into a ratio of 3:5. 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. Note: Directed line segment – tells the direction in terms of which point to start and end. In this case, from A to B.

Example 2 Find Q along the directed line segment from R(-3, 3) to S(6, -3) that divides the segment into the ratio 2 to 1.

Example 3 Find Q along the directed line segment from R(-2, 4) to S(18, -6) that divides the segment into the ratio 3 to 7.

You try! Find P along the directed line segment from A(1, 1) to B(7, 3) that divides the segment into the ratio 1:4.

You Try Again! Find P along the directed line segment from A(3, -3) to B(4, 2) that divides the segment into the ratio 3 to 2.

Assignment: Partitioning Segment worksheet