Question

Given a line segment AB joining the points A (-4, 6) and B (8, -3). Find:
(i) the ratio in which AB is divided by the y-axis.
(ii) find the coordinates of the point of intersection.

Answer 1

Answer:

${ \large{ \pmb{ \sf{★Given... </p><p>}}}}$

A(-4, 6)

B(8, -3)

${ \large{ \pmb{ \sf{★To \: Find... </p><p>}}}}$

(i) The ratio in which AB is divided by the y-axis.

(ii) Find the coordinates of the point of intersection.

${ \large{ \pmb{ \sf{★ Solution...}}}}$

(I) :

By using section formula:

$\boxed{ \sf{ \bigg( \frac{m x_{2} + n x_{1}}{m + n}, \frac{my_{2} + ny_{1}}{m + n} \bigg)}}$

A(-4 , 6) = (x1, y1)

B(8, -3) = (x2, y2)

The equation of your axis is (0, y)

By substituting,

${ \implies{ \sf{ \bigg( \frac{m(8) + n( - 4)}{m + n} , \frac{m( - 3) + n(6)}{m + n} \bigg) = (0, y) }}}$

$\: { \implies{ \sf{ \bigg( \frac{8m - 4n}{m + n} , \frac{ - 3m + 6n}{m + n} \bigg) = (0, y)}}}$

${ \implies{ \sf{ \frac{8m - 4n}{m + n} = 0}}}$

${ \implies{ \sf{8m - 4n = 0}}}$

${ \implies{ \sf{8m = 4n}}}$

${ \implies{ \sf{ \frac{m}{n} = \frac{4}{8} = \frac{1}{2} }}}$

${ \implies{ \bf{m: n = 1 :2}}}$

_________________________________

(ii) :

By using section formula substitute m and n values:

${ \implies{ \sf{ \bigg( \frac{1(8) + 2( - 4)}{1 + 2} , \frac{1( - 3) + 2(6)}{1 + 2} \bigg)}}}$

$\: { \implies{ \sf{ \bigg( \frac{8 + ( - 8)}{3} , \frac{ - 3 + 12}{3} \bigg)}}}$

$\: { \implies{ \sf{ \bigg( \frac{0}{3} , \frac{9}{3} \bigg)}}}$

$\: { \implies{ \sf{ (0, 3)}}}$

Therefore,

(I) 1 : 2 the ratio in which AB is divided by the y-axis.

(ii) (0, 3) are the coordinates of the point of intersection.

Answer 2

Step-by-step explanation:

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