Question

Find the co-ordinates of the point P which divides the join of
A(-2,5) and B(3,-5) in the ratio 2:3​

Answer 1

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Answer 2

Answer:

Explanation:

Given :

• The point P which divides the join of
• A(-2,5) and B(3,-5) in the ratio 2:3.

To Find :

• The co-ordinate of the point P.

Formula to be used :

• Section formula, ie,, x = (mx2 + nx1/m + n) and y = (my2 + ny1/m + n).

Solution :

$\setlength{\unitlength}{1cm}\begin{picture}(10,6)\thicklines\put(2,3){\line(1,0){2}}\put(3,3){\line(1,0){4}}\put(2,3){\circle*{0.15}}\put(4,3){\circle*{0.15}}\put(7,3){\circle{0.15}}\put(1.5,2.5){\sf{A(-2,5)}} \put(3.5,2.5){\sf{P(x,y)}} \put(6.5,2.5){\sf{B(3,-5)}}\put(3,3.2){\sf{2}}\put(5.3,3.2){\sf{3}}\end{picture}$

Here,

• m = 2
• n = 3
• x1 = -2
• y1 = 5
• x2 = 3
• y2 = -5

★ x co - ordinate,

x = (mx2 + nx1/m + n)

⇒ x = (2 × 3 + 3 × -2/ 2 + 3)

⇒ x = (6 - 6 /5)

⇒ x = (0/5)

⇒ x = 0

★ y co - ordinate,

y = (my2 + ny1/m + n)

⇒ y = (2 × -5 + 3 × 5/ 2 + 3)

⇒ y = (-10 + 15/ 5)

⇒ y = (5/5)

⇒ y = 1

.°. P(x,y) = (0,1)

Hence, The co-ordinate of the point P is (0,1).