Activity for Finding Distances on



Activity for Finding Distances on

Number Lines and the Coordinate System

Name_____________________________________period_____________date_____________

1. Definition of a point being between two other points

Let’s explore what it means for a point to be between two other points.

• Draw a sketch of three points, A, B, and C where B is between points A and C.

• Draw a sketch of three points, A, B, and C where B is not between points A and C

• To say that point B is between points A and C, is it enough to say that [pic] Why or why not?

• What statement must we make to insure that point B is between points A and C?

2. Finding the distance between two points on a number line

The definition for a point being between two other points states that we need to know the distance between the points. We could use a ruler, but when points are on number lines, rulers are not always useful.

Below is a number line.

X Y

[pic]

-17 0 23

• Find the distance from point X to point Y.

(Leave off the segment bar if you mean length of the segment.) XY = _________

• Show how you could calculate this length or distance using arithmetic.

• Switch the numbers around in the problem you just wrote. Take the absolute value of the answer.

• State in words and mathematical symbols how we find the length of a segment or distance between two points on a number line.

• Find the distance between the following points on a number line. Use the formula from above. Show Work.

(a) -23, 45 (b) -34, -87 (c) 567, 765 (d) -981, 23

3. Finding the distance between two points on the coordinate plane

• Below are segments drawn on a coordinate plane. By sketching both a horizontal and a vertical broken line, each segment has become the _____________________ of a right triangle.

• Circle two segments from the above graph and find the length or distance of the segments. Show work below. (Hint: Use the Pythagorean Theorem.)

• Suppose you have a segment where the coordinates of the endpoints of the segment are too large for your graph paper? An example would be points (15, 37) and (42, 73).

Use the Pythagorean Theorem to find the length of this segment.

• Recopy the following statements replacing the question marks with x’s and y’s to show the distance formula that is often used to find the length of a segment on a coordinate graph.

If the coordinates of points A and B are [pic] respectively then the length of the segment AB (or the distance between points A and B) can be shown as

[pic] or [pic]

• Use the above formula and find the distance between each pair of points. Show Work.

(a) (10, 20) (13, 16) (b) (15, 37) (42, 73) (c) (-19, -16) (-3, 14) (d) (0,30) (50,0)

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