Question

Find the point on y-axis whose distances from the points A (6, 7) and B (4, -3) are in the ratio 1: 2.

Answer 1

Step-by-step explanation:

Dear student

Let the coordinate of the point at x – axis be (x, 0).

Let the ratio be m : n.

Applying section formula,

Putting (x 1, y 1) = (6,4), (x 2, y 2) = (1,-7) and (x, y) = (x, 0)

x=1m+6nm+n,0=−7m+4nm+nTaking 0=−7m+4nm+n⇒−7m+4n=0⇒7m=4n⇒mn=47So, m:n=4:7Thus, line segment joining (6,4) and (1,−7) is divided by x−axis in the ratio 4:7

Distance 2AB=2(1−6)2+(−7−4)2−−−−−−−−−−−−−−−−−√=252+112−−−−−−−√=225+121−−−−−−−√=2146−−−√

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