Find the ratio in which the line segment joining the points A(6,4) and B(1,-7) is divided by the x axis . Also find the distance 2AB and the coordinates of the point on the x axis which cuts the line segment joining A and B in the required ratio

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=07m=4nmn=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=21-62+(-7-4)2=252+112=225+121=2146
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