<meta http-equiv="refresh" content="1; url=/nojavascript/"> Distance Between Two Points ( Read ) | Geometry | CK-12 Foundation
Dismiss
Skip Navigation
You are viewing an older version of this Concept. Go to the latest version.

Distance Between Two Points

%
Best Score
Practice Distance Between Two Points
Practice
Best Score
%
Practice Now
Distance Between Two Points
 0  0  0 Share To Groups

What if you were given the coordinates of two points that form either a vertical or horizontal line? How would you determine how far apart those two points are? After completing this Concept, you'll be able to determine the distance between two such points.

Watch This

CK-12 Measuring Distances

James Sousa: Ruler Postulate and Segment Addition Postulate

Guidance

Distance is the measure of length between two points. To measure is to determine how far apart two geometric objects are. The most common way to measure distance is with a ruler. Inch-rulers are usually divided up by eighth-inch (or 0.125 in) segments. Centimeter rulers are divided up by tenth-centimeter (or 0.1 cm) segments. Note that the distance between two points is the absolute value of the difference between the numbers shown on the ruler. This implies that you do not need to start measuring at “0”, as long as you subtract the first number from the second.

The segment addition postulate states that if A , B , and C are collinear and B is between A and C , then AB + BC = AC .

You can find the distances between points in the xy plane if the lines are horizontal or vertical. If the line is vertical, find the change in the y- coordinates. If the line is horizontal, find the change in the x- coordinates.

Example A

What is the distance marked on the ruler below? The ruler is in centimeters.

Subtract one endpoint from the other. The line segment spans from 3 cm to 8 cm. |8 - 3| = |5| = 5

The line segment is 5 cm long. Notice that you also could have done |3 - 8| = |-5| = 5 .

Example B

Make a sketch of \overline{OP} , where Q is between O and P .

Draw \overline{OP} first, then place Q on the segment.

Example C

What is the distance between the two points shown below?

Because this line is vertical, look at the change in the y- coordinates.

|9 - 3| = |6| = 6

The distance between the two points is 6 units.

CK-12 Measuring Distances

Guided Practice

1. Draw \overline{CD} , such that CD = 3.825 \ in .

2. In the picture from Example B, if OP = 17 and QP = 6 , what is OQ ?

3. What is the distance between the two points shown below?

Answers:

1. To draw a line segment, start at “0” and draw a segment to 3.825 in.

Put points at each end and label.

2. Use the Segment Addition Postulate.

OQ + QP & = OP\\OQ + 6 & = 17\\OQ & = 17-6\\OQ & = 11

3. Because this line is horizontal, look at the change in the x- coordinates.

|(-4) - 3| = |-7| = 7

The distance between the two points is 7 units.

Practice

For 1-4, use the ruler in each picture to determine the length of the line segment.

  1. Make a sketch of \overline{BT} , with A between B and T .
  2. If O is in the middle of \overline{LT} , where exactly is it located? If LT = 16 \ cm , what is LO and OT ?
  3. For three collinear points, A between T and Q :
    1. Draw a sketch.
    2. Write the Segment Addition Postulate for your sketch.
    3. If AT = 10 \ in and AQ = 5 \ in , what is TQ ?
  1. For three collinear points, M between H and A :
    1. Draw a sketch.
    2. Write the Segment Addition Postulate for your sketch.
    3. If HM = 18 \ cm and HA = 29 \ cm , what is AM ?
  1. For three collinear points, I between M and T :
    1. Draw a sketch.
    2. Write the Segment Addition Postulate for your sketch.
    3. If IT = 6 \ cm and MT = 25 \ cm , what is AM ?
  1. Make a sketch that matches the description: B is between A and D . C is between B and D . AB = 7 \ cm, \ AC = 15 \ cm , and AD = 32 \ cm . Find BC, BD , and CD .
  2. Make a sketch that matches the description: E is between F and G . H is between F and E . FH = 4 \ in, \ EG = 9 \ in , and FH = HE . Find FE, HG , and FG .

For 12 and 13, Suppose J is between H and K . Use the Segment Addition Postulate to solve for x . Then find the length of each segment.

  1. HJ = 4x + 9, \ JK = 3x + 3, \ KH = 33
  2. HJ = 5x - 3, \ JK = 8x - 9, \ KH = 131

For 14-17, determine the vertical or horizontal distance between the two points.

  1. Make a sketch of: S is between T and V . R is between S and T . TR = 6, RV = 23 , and TR = SV .
  2. Find SV, TS, RS and TV from #18.
  3. For \overline{HK} , suppose that J is between H and K . If HJ = 2x + 4, \ JK = 3x + 3 , and KH = 22 , find x .

Image Attributions

Reviews

Email Verified
Well done! You've successfully verified the email address .
OK
Please wait...
Please wait...
ShareThis Copy and Paste

Original text