Concept explainers
To find: the coordinate of a point located between two given points on a number line.
Answer to Problem 58WE
The coordinate of the point between C and D with the given condition is 2
Explanation of Solution
Given Information: Point C and D are located on the number line with coordinates -2 and 4 respectively. An unknown point is located between C and D such that its distance from C is twice its distance from D
A number line is used to graphically represent numbers along a line. It consists of 0 as the center point. The positive numbers are marked to the right and negative numbers are marked to the left side of the center point.
The given points are C and D which are located at - 2 and 4 respectively. The number line and the given numbers marked on it are as shown below.
1. Let the distance between the point D and the unknown point be x.
2. Then the distance between the unknown point and the point C is 2x.
3. Also, the sum of the distance x and 2 x forms the distance between the points C and D. The distance between C and D has to be calculated considering the magnitude only. Here, it is the sum of 2 units corresponding to distance from point C to origin and then 4 units corresponding to distance between origin and point D..
Thus, the distance between C and D can be represented as,
The above value of x implies that, the unknown point is located at a distance of 2 units from point D towards C and 4 units from point D towards C. Thus the coordinate of the desired point is at 2. This is shown in Figure 2.
Chapter 1 Solutions
Algebra: Structure And Method, Book 1
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