Question

find the ratio in which the join of (-4,7) and (3,0) is divided by the by y axis also find the point of intersection

Answer 1

Correct question :-

Find the ratio in which the line segment formed by joining the points (-4,7) and (3,0) is divided by the y - axis. Also find the point of intersection.

Solution :-

The line segment is formed by joining (-4,7) and (3,0) and is divided by y - axis

The general form of coordinates of y axis are (0,y)

So, (0,y) divided the line segment formed by joining points (-4,7) (3,0)

Let the ratio which divides the line segment be m : n

By using section formula

$P(x,y) = \bigg( \dfrac{mx_2 + nx _1 }{m + n},\dfrac{my_2 + ny _1 }{m + n} \bigg)$

(-4,7) (3,0)

Here,

• x1 = -4
• y1 = 7
• x2 = 3
• y2 = 0

By substituting the coordinates of y - axis and the values

$\implies P(0,y) = \bigg( \dfrac{m(3) + n( - 4) }{m + n},\dfrac{m(0) + n(7) }{m + n} \bigg)$

$\implies P(0,y) = \bigg( \dfrac{3m - 4n }{m + n},\dfrac{ 7n }{m + n} \bigg)$

Equating x - coordinates

⇒ 0 = (3m - 4n)/(m + n)

⇒ 0(m + n) = 3m - 4n

⇒ 0 = 3m - 4n

⇒ 4n = 3m

⇒ 4/3 = m/n

⇒ m/n = 4/3

⇒ m : n = 4 : 3

Therefore the line segment is divided in the ratio of 4 : 3

Equating y- coordinates

⇒ y = 7n/(m + n)

⇒ y = 7(3) / (4 + 3)

[ Because m : n = 4 : 3, m = 4, n = 3 ]

⇒ y = 7(3) / 7

⇒ y = 3

Therefore the point of intersection is (0,3).