Question

9.The line segment AB joining the points A(3,-4) and B(1,2) is trisected at the points P(p,-2)
and Q (5,9).Find the values of p and q​

Answer 1

Answer:

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Answer 2

Suppose Points P and Q trisect the line segment joining the pointsA(3,−4) and B(1,2)

This means, P divides AB in the ratio 1:2 and Q divides it in the ratio 2:1

Using the section formula, if point (x,y) divides the line joining the points (x1,y1) and (x2,y2) internally in the ratio m:n, then(x,y)=(m+nmx2+nx1,m+nmy2+ny1)

Substituting (x1,y1)=(3,−4) and (x2,y2)=(1,2)  and m=1,n=2 in the section formula, we get the point P =(1+21(1)+2(3),1+21(2)+2(−4))=(37,−2)

Given. P(p,−2)=(37,−2)

=>p=