   # Now suppose that we want to find the coordinates of point P , which is located two-thirds of the distance from A ( 1 , 2 ) to B ( 7 , 5 ) in a coordinate plane. We have plotted the given points A and B in Figure 7.36 to help with the analysis of this problem. Point D is two-thirds of the distance from A to C because parallel lines cut off proportional segments on every transversal that intersects the lines. Figure 7.36 Thus A C ¯ can be treated as a segment of a number line, as shown in Figure 7.37. Therefore, x = 1 + 2 3 ( 7 − 1 ) = 1 + 2 3 ( 6 ) = 5 Figure 7.37 Similarly, C B ¯ can be treated as a segment of a number line, as shown in Figure 7.38. Therefore, y = 2 + 2 3 ( 5 − 2 ) = 2 + 2 3 ( 3 ) = 4 The coordinates of the point P are ( 5 , 4 ) . Figure 7.38 For each of the following, find the coordinates of the indicated point in the x y plane. (a) One-third of the distance from ( 2 , 3 ) to ( 5 , 9 ) (b) Two-thirds of the distance from ( 1 , 4 ) to ( 7 , 13 ) (c) Two-fifths of the distance from ( − 2 , 1 ) to ( 8 , 11 ) (d) Three-fifths of the distance from ( 2 , − 3 ) to ( − 3 , 8 ) (e) Five-eighths of the distance from ( − 1 , − 2 ) to ( 4 , − 10 ) (f) Seven-eighths of the distance from ( − 2 , 3 ) to ( − 1 , − 9 ) ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

#### Solutions

Chapter
Section ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter 7.3, Problem 69PS
Textbook Problem
1 views

## Now suppose that we want to find the coordinates of point P, which is located two-thirds of the distance from A ( 1 , 2 ) to B ( 7 , 5 ) in a coordinate plane. We have plotted the given points A and B in Figure 7.36 to help with the analysis of this problem. Point D is two-thirds of the distance from A to C because parallel lines cut off proportional segments on every transversal that intersects the lines.Figure 7.36Thus A C ¯ can be treated as a segment of a number line, as shown in Figure 7.37. Therefore, x = 1 + 2 3 ( 7 − 1 ) = 1 + 2 3 ( 6 ) = 5 Figure 7.37Similarly, C B ¯ can be treated as a segment of a number line, as shown in Figure 7.38. Therefore, y = 2 + 2 3 ( 5 − 2 ) = 2 + 2 3 ( 3 ) = 4 The coordinates of the point P are ( 5 , 4 ) . Figure 7.38For each of the following, find the coordinates of the indicated point in the x y plane.(a) One-third of the distance from ( 2 , 3 ) to ( 5 , 9 ) (b) Two-thirds of the distance from ( 1 , 4 ) to ( 7 , 13 ) (c) Two-fifths of the distance from ( − 2 , 1 ) to ( 8 , 11 ) (d) Three-fifths of the distance from ( 2 , − 3 ) to ( − 3 , 8 ) (e) Five-eighths of the distance from ( − 1 , − 2 ) to ( 4 , − 10 ) (f) Seven-eighths of the distance from ( − 2 , 3 ) to ( − 1 , − 9 )

(a)

To determine

To find:

The coordinates of the point in the xy plane.

### Explanation of Solution

Given:

The given information is that the two points are (2,3) and (5,9).

The required distance is one-third of the given points,

Calculation:

From the given information, the two points are (2,3) and (5,9).

The required distance is 13 of the distance between (2,3) and (5,9).

Let the required coordinates be (x,y).

The value of x is given by,

(b)

To determine

To find:

The coordinates of the point in the xy plane.

(c)

To determine

To find:

The coordinates of the point in the xy plane.

(d)

To determine

To find:

The coordinates of the point in the xy plane.

(e)

To determine

To find:

The coordinates of the point in the xy plane.

(f)

To determine

To find:

The coordinates of the point in the xy plane.

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