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Chapter 10: Q53. (page 659)

Find the distance between points with the given coordinates and the midpoint of the segment with the given endpoints. Round to the nearest hundredth if necessary.

2,4,鈭�3,4

Short Answer

Expert verified

The distance between the points2,4 and鈭�3,4 is 5.

The midpoint of the line segment with the endpoints at2,4 and鈭�3,4 is 鈭�0.5,4.

Step by step solution

01

Step 1. Given.

Coordinates are2,4 and鈭�3,4

02

Step 2. Find the distance between the points 2,4 and −3,4.

The distance (d) between the pointsx1,y1 andx2,y2 is given by:

d=x2鈭�x12+y2鈭�y12

Therefore, the distance (d) between the points2,4 and鈭�3,4 is:

d=鈭�3鈭�22+4鈭�42=鈭�52+02=25+0=25=52=5

Therefore, the distance (d) between the points2,4and 鈭�3,4is 5.

03

Step 3. Find the midpoint of the segment with the endpoints at 2,4 and −3,4.

The midpoint formula states that the midpoint M of a line segment with endpoints at x1,y1andx2,y2 is given by M=x1+x22,y1+y22.

The midpoint (M) of the line segment with endpoints at2,4 and鈭�3,4 is given by:

M=x1+x22,y1+y22=2+鈭�32,4+42=2鈭�32,82=鈭�12,4=鈭�0.5,4

Therefore, the midpoint of the line segment with the endpoints at2,4 and鈭�3,4 is 鈭�0.5,4.

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