1-3 Distance and Midpoints

1-3 Distance and Midpoints You graphed points on the coordinate plane. • Find the distance between two points. • Find the midpoint of a segment.

The distance between two points is the length of the segment with those points as its endpoints. Distance is ALWAYS positive in math. p. 25

Find Distance on a Number Line Use the number line to find QR. The coordinates of Q and R are –6 and –3. QR = | –6 – (–3) | Distance Formula = | –3 | or 3 Simplify. Answer: 3

Use the number line to find AX. A. 2 B. 8 C. –2 D. –8

Distance Formula p. 26 You will need a scientific calculator to do this problem • Put x’s and y’s in the formula • Subtract x’s and square • Subtract y’s and square • Add numbers under the radical • Take square root if answer is in decimal form.

(x1, y1) = (–4, 1) and (x2, y2) = (3, –1) Find Distance on a Coordinate Plane Find the distance between E(–4, 1) and F(3, –1).

A.4 B. C. D. Find the distance between A(–3, 4) and M(1, 2).

1-3 Assignment Day 1 p. 31, 13-31 odd No work, No credit!

1-3 Distance and Midpoints Day 2 You graphed points on the coordinate plane. • Find the distance between two points. • Find the midpoint of a segment.

Midpoint Definition The midpoint of a segment is the point halfway between the end points of the segment. A B M M is the midpoint of (reads line segment AM is congruent to line segment MB

Midpoint Formula p. 27 • Add the x’s and divide by 2 • Add the y’s and divide by 2

Find Midpoint on a Number Line DECORATING Marco places a couch so that its end is perpendicular and 2.5 feet away from the wall. The couch is 90” wide. How far is the midpoint of the couch back from the wall in feet? First we must convert 90 inches to 7.5 feet. The coordinates of the endpoints of the couch are 2.5 and 10. Let M be the midpoint of the couch. Midpoint Formula x1 = 2.5, x2 = 10 Simplify. Answer: The midpoint of the couch back is 6.25 feet from the wall.

DRAG RACING The length of a drag racing strip is mile long. How many feet from the finish line isthe midpoint of the racing strip? A. 330 ft B. 660 ft C. 990 ft D. 1320 ft 1 mile = 5280 feet

Coordinate Plane Midpoint Formula Same formula, but… Use it for the x coordinates. Use it for the y coordinates.

Find Midpoint in Coordinate Plane Answer: (–3, 3)

A. (–10, –6) B. (–5, –3) C. (6, 12) D. (–6, –12)

(x2, y2) = (–5, –3) Find the Coordinates of an Endpoint Let D be (x1, y1) and F be (x2, y2) in the Midpoint Formula. Write two equations to find the coordinates of D.

Midpoint Formula Midpoint Formula Answer: The coordinates of D are (–7, 11).

Find the coordinates ofRifN (8, –3) is the midpointofRSandShas coordinates (–1, 5). A. (3.5, 1) B. (–10, 13) C. (15, –1) D. (17, –11) hint: = -3 = 8

PlanBecause Q is the midpoint, you know that UnderstandYou know that Q is the midpoint of PR, and the figure gives algebraic measures for QR and PR. You are asked to find the measure of PR. Use Algebra to Find Measures

Subtract 1 from each side. Use this equation and the algebraic measures to find a value for x. Solve

Original measure

What does the word bisect mean? Bi means: two An area or portion, subdivision Sector means: Bisect – divide into 2 equal parts Segment Bisector A segment bisector is any segment, line, or line that intersects a segment at its midpoint.

Construction: Bisect a Segment • Draw a segment. • Place the compass on one end and open the compass bigger than half of the segment. • Draw arcs above and below the segment. • Without moving the compass sixe, move the point to the other end of the segment. • Draw arcs about and below the segment. • Use a straightedge to connect the x’s you made above and below the segment. • Where this new segment crosses the 1st one is the midpoint. • See page 30 for pictures.

Assignment 1-3 p. 31, 28-30 even, 33-41 odd, 47,49 No work, No credit

1-3 Distance and Midpoints