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Chapter 10: Q23. (page 661)

Find the coordinates of the midpoint of the segment with the given endpoints.

(鈭�4,鈭�8),鈥�(10,鈭�6)

Short Answer

Expert verified

The coordinates of the midpoint of the segment with the given endpoints is(3,鈭�7).

Step by step solution

01

Step 1. State the concept of ‘midpoint of a segment in 2 dimensional plane’.

Let the two points in 2 dimensional plane be(x1,y1)and(x2,y2).

The midpoint of the segment with endpoints is given as:

(x,y)=x1+x22,y1+y22鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌�鈥�(1)

Where(x,y)is the midpoint.

02

Step 2. Calculate the distance.

The two points which is given are(鈭�4,鈭�8)and(10,鈭�6).

Substitute(鈭�4,鈭�8)as(x1,y1)and(10,鈭�6)as(x2,y2)in (1) to calculate the distance.

localid="1647929305709" (x,y)=x1+x22,y1+y22=鈭�4+102,鈭�8+(鈭�6)2=62,鈭�8鈭�62=62,鈭�142=(3,鈭�7)

03

Step 3. State the conclusion.

Therefore, midpoint of the segment with the endpoints (鈭�4,鈭�8) and(10,鈭�6) is (3,鈭�7).

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