Question

In what ratio does the point P(1,3) divide the line segment joining the points A(-1,7) and B(4,-3)?​

Answer 1

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Let p(p,-1) divide the join of A(1,-3) and B(6,2) in the ratio K:1.

The co-ordinate of p are (m1x2 + m2x1)/(m1+m2), (m1y2+m2y1/(m1+m2)

= (6K + 1)/(k+1), (2k-3)/(k+1)

But co-ordinates of p are (p,-1)

2k-3/k+1 = -1

2k -3 = -k -1

2k + k = -1+3

3k = 2

k = 2/3

6k +1 / k+1 = p

(6 x 2/3 +1)/(2/3 +1) = p

(4 +1)/ (5/3) = p

5/(5/3) = p

15/5 = p

p = 3

Substituting k = 2/3 p = 3

Ratio of division is 2/3 : 1 and p = 3.

Answer 2

Answer:

prefer the above answer