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Answer:

The co- ordinate of B is (0, 3).

Step-by-step EXPLANATION:

It is given that

AC = 6AB

or AB + BC = 6AB

or BC = 6AB - AB

or BC = 5 AB

or AB/ BC = 1/5

Hence B divides AC internally in the ratio 1:5

Co- ordinate of a point which divides the line joining (x₁, y₁) and (x₂, y₂) internally in the ratio m:n is given by

(x,y) = ( (mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n) )

Hence, co-ordinate of B is given by

( \frac{1 \times ( - 5) + 5 \times 1}{1 + 5} \: \: \: \: \: \:\frac{1 \times ( - 7) + 5 \times 5}{1 + 5} )

= ( \frac{ - 5 + 5}{6} \: \: \: \frac{ - 7 + 25}{6} )

= (0 \: \: \: \: \frac{18}{6} )

= (0, 3)


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