Question

A point P(-2,3) divides the line segment joining the
paints A(-4,5) and B(3,-2) in the ratio of​

Answer 1

Step-by-step explanation:

Given:A point P(-2,3) divides the line segment joining the points A(-4,5) and B(3,-2) in the ratio of ?

To find: Ratio of division

Solution:

To find the ratio,we have to apply section formula

If Point P(x,y) divides the points A(x1,y1) and B(x2,y2) in m:n

then

Coordinates of P are

$x = \frac{mx_2 + nx_1}{m + n} \\ \\ y = \frac{my_2 + ny_1}{m + n}$

Apply section formula with given points

$- 2 = \frac{3m - 4n}{m + n} \\ \\ - 2(m + n) = 3m - 4n \\ \\ - 2m - 3m = - 4n + 2n \\ \\ - 5m = - 2n \\ \\ 5m = 2n \\ \\ \bold{\frac{m}{n} = \frac{2}{5} }$

Thus,

Point P divides the line segment joining points A and B in 2:5

Hope it helps you.

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Answer 2

Given:-

• A point P(-2,3) divides the line segment joining the points A(-4,5) and B(3,-2) .

To find:-

• The ratio.

Solution:-

We know,

Section formula :

If Point P(x,y) divides the points A(x1,y1) and B(x2,y2) in m:n,

Coordinates of P are :

$\sf \pink{\begin{gathered}✷x = \frac{mx_2 + nx_1}{m + n} \\ \\ ✷y = \frac{my_2 + ny_1}{m + n} \\ \\\end{gathered}}$

Substituting the values in the formula :

$\sf \implies - 2 = \frac{3m - 4n}{m + n}$

$\sf \implies - 2(m + n) = 3m - 4n$

$\sf \implies - 2m - 3m = - 4n + 2n$

$\sf \implies - 5m = - 2n$

$\sf \implies 5m = 2n$

$\sf \implies \bold{ \purple{ m /n = 2/6 }}$

Therefore,

Point P divides the line segment joining points A and B in the ratio of $\underline{\pink{2:5}}$

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