Activity on Finding Midpoints of Segments

Name ______Period ______Date ______

ACTIVITY ON FINDING MIDPOINTS OF SEGMENTS

A. Finding the location of midpoints using various methods.

1. Find the midpoint of segment AB using the method of paper folding. Label the midpoint, M. Write a mathematical statement about the two congruent ( ) segments. ______

2. Find the midpoint of segment CD using the Mira or geomirror. Label the midpoint, X. Write a mathematical statement about the two congruent () segments. ______Draw the line that intersects segment CD. This line is called a ______of the segment. This line also creates four right angles at the point of intersection. Mark these four right angles using the symbol for a right angle. The line you drew is called the ______of the segment.

3. Find the midpoint of segment EF using the compass. Label the midpoint, Y. Write a mathematical statement about the two congruent () segments. ______Draw the line that intersects segment EF. This line is called a ______of the segment. Mark the right angles.

4. Find the midpoint of segment GH using the ruler. Measure segment GH to the nearest eighth of an inch. The length of segment GH is approximately ______inches. Find the midpoint of segment GH by dividing the length in half. One half of segment GH is ______inches. Measure this distance on segment GH and label it point Z. Write a mathematical statement about the two congruent () statements. ______

B. Finding the coordinates of midpoints on number lines.

1. Find the midpoint of segment QT using mathematics. Point Q is located on the number line at -23 and point T is located on the number line at 45. Show how you arrived at your answer.

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2. Referring to problem #1, suppose point Q is located at -87 on the number line and point T is located at -198 on the number line. Find the midpoint of QT. Show how you arrived at your answer.

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3. Again referring to problem #1, suppose point Q is located at 235 on the number line and point T is located at point 1458. Find the midpoint of QT. Show how you arrived at your answer.

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4. Suppose the endpoint of a segment on the number line is x1 and the other endpoint is x2.

Write a mathematical formula showing how the location of the midpoint can be found.

C. Finding the coordinates of midpoints on the coordinate plane.

1. (a) Draw the following segments on the coordinate graph below.

(b) Find and complete:

Coordinate of point Coordinate of point Coordinate of midpoint of segment

O ( , ) L ( , ) OL ( , )

L ( , ) N ( , ) LN ( , )

O ( , ) N ( , ) ON ( , )

(c) Draw a segment from (3, 0) to (3, -3)

Draw a segment from (3,-3) to (6, -3)

(d) Considering the x axis as a number line

and the y axis as a number line, how

could you use the formula you wrote

under number 4 on the previous page

to find the coordinate of the midpoint

of segment ON?

2. If the coordinates of one point are ( x1 , y1) and the coordinates of another point are ( x2 , y2) then write a mathematical formula for finding the midpoint of the segment.

D. Finding the other endpoint of a segment when one endpoint and the midpoint is known.

1. Given points Q and R below. Q is one end of a segment and R is the midpoint. Find the other

endpoint of the segment using the graph. The coordinate of the other endpoint is ( , ).

2. Find the coordinate of the other endpoint using algebra and the formula for the midpoint of a segment as you discovered in C. 2.