How do we find the distance between two coordinate points?

Requirements: full explanation and answers

Geometry Name____________________

Period____ Date_____________________

Distance and Midpoint Formulas

Objective for lesson:

1. Master the distance formula

2. Master the midpoint formula

3. Apply the two formulas together to more complicated questions

Essential Questions:

How do we find the distance between two coordinate points?

How do we find the coordinates of a midpoint ?

Do Now :

Guided Practice:

Topic One: Distance Formula

1. Distance formula is one you just have to memorize and never forget because you’re going to use it forever, in all math classes

2. The distance between the points

Tutorial Video: Distance Formula

Example :

To find the distance between the points P(2, 3) and Q(1, 1).

We can sketch the right-angled triangle PQR with PQ as the hypotenuse.

You Try:

Find the distance between the points (2, 5) to (3, 1)

Topic Two: Midpoint Formula

1. Similar to distance formula, midpoint formula is one you just have to memorize and practice over and over

2. The midpoint of

Tutorial Video: Midpoint Formula

Example :

Find the midpoint of the two points A(1, -3) and B(4, 5).

Solution:

You Try!

Find the midpoint of the two following points (1, 3) (3, 11)

Concept Summary:

Independent Practice:

1- As shown, a path goes around a triangular park.

a. Find the distance around the park to the nearest yard.

b. A new path and a bridge are constructed from point Q to the midpoint M of PR. Find QM to the nearest yard.

2- If the distance between (0, 1) and (x, 4) is √34, then solve for x.

3- (-1, -3) is the midpoint of (8, -5) and (x, y). Solve for (x, y).

Name __________________________________ Hour _______Distance Formula WorksheetName ______________________________________ Hour ________1-3 Distance Formula Day 1WorksheetCONSTRUCTIONSDirections for constructing a perpendicular bisector of a segment.1)Place the compass at one end of the line segment and open it wider than half way2)Draw an arc that is almost the size of a semi circle3)Without changing the compass settings, place the compass at the other end of the line segment and draw another arc that intersects the first arc.4)Draw a line connecting the intersections of the arc. This is the perpendicular bisector.Draw each perpendicular bisector.1.