Question

Find the coordinates of a point dividing AB In the ratio 3:2 where A is point (6, -3) and B (-2, 4)

Answer 1

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GiveN:

• Coordinates of Point A and Point B are (6,-3) and (-2,4)
• Ratio in which they are divided = 3:2

To FinD:

• Coordinates of Point which divides the line joining AB in ratio 3:2?

Step-wise-Step Explanation:

Let P(x,y) be the required point.

A(6,-3) and B(-2,4) are the end points of line.

Then,

• x1 = 6
• y1 = -3
• x2= -2
• y2 = 4

We will solve the above by using Section's formula:

Point which divides the line segment joining the points (x1,y1) and (x2,y2) in the ratio m:n is given by:

$\boxed{\rm{x = \frac{mx2 + nx1}{m + n} }} \boxed{ \rm{y = \frac{my2 + ny1}{m + n} }}$

By putting the required values to get the points:

$\rm{ x = \dfrac{3 \times - 2 + 2 \times 6}{3 + 2} }$

$\rm{x = \dfrac{ - 6 + 12}{5} }$

$\rm{x = \dfrac{6}{5} }$

And now,

$\rm{y = \dfrac{3 \times 4 + 2 \times - 3}{3 + 2} }$

$\rm{y = \dfrac{12 - 6}{5} }$

$\rm{ y = \dfrac{6}{5} }$

Hence,

• The required coordinates of Point P which divides the line segment AB in ratio 3:2 is (6/5, 6/5)

Answer 2

Step-by-step explanation:

Given :

• A is point (6, -3) and B (-2, 4)

To Find :

• Find the coordinates of a point dividing AB In the ratio 3:2

Solution :

According to the Question :

• x1 = 6

• x2= -2

• y1 = -3

• y2 = 4

• m = 3

• n = 2

Concept :

• The section formula tells us the coordinates of the point which divides a given line segment into two parts such that their lengths are in the ratio m : n m:n m:n. .The section formula is helpful in coordinate geometry; for instance, it can be used to find out the centroid, incenter and excenters of a triangle.

First we find the value of x

• x = (m1x2 + m2x1) / m1 + m2

Substitute all values :

x = [ 3 × ( - 2 ) + 2 × 6 ] / 3 + 2

• When 3 multiplied by - 2 is equal to 6 and 2 multiplied by 6 is equal to 12

x = [ - 6 + 12 ] / 3 + 2

x = 6 / 5

we find the value of y

• y = (m1y2 + m2y1) / m1 + m2

Substitute all Values :

y = [ 3 × 4 + 2 × ( - 3 ) ] / 3 + 2

• When 3 multiplied by 4 is equal to 12 and 2 multiplied by - 3 is equal to 6

y = [ 12 - 6 ] / 5

y = 6/ 5

x = 6/5 and y = 6/5 the coordinates of a point dividing AB In the ratio 3: 2

More to know :

Coordinate geometry :

• Coordinate geometry is one of the most important and exciting ideas of mathematics.

• In particular it is central to the mathematics students meet at school.

• It provides a connection between algebra and geometry through graphs of lines and curves.