Point P divides a line segment joining<br />the points A(-5, 2) and B(-12, -5)<br />AP k<br />such that<br />PB 1<br />Also, P lies on x-axis.<br />Find the value of k.<br />k
Answers
Step-by-step explanation:
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Step-by-step explanation:
Let the line segment A(5, -6) and B(-1, -4) is divided at point P(0, y) by y-axis in ratio m:n
:. x = \frac{mx2+nx1}{m+n
and y = \frac{my2+ny1}{m+n
Here, (x, y) = (0, y); (x1, y1) = (5, -6) and (x2, y2) = (-1, -4)
So , 0 = \frac{m(-1)+n(5)}{m+n}
=> 0 = -m + 5n
=> m= 5n
=> \frac{m}{n}
= \frac{5}{1}
=> m:n = 5:1
Hence, the ratio is 5:1 and the division is internal.Now,
y = \frac{my2+ny1}{m+n}
=> y = \frac{5(-4)+1(-6)}{5+1}
=> y = \frac{-20-6}{6}
=> y = \frac{-26}{6}
=> y = \frac{-13}{3}
Hence, the coordinates of the point of division is (0, -13/3).