Question

Find the coordinates of the point which divides the join of (-1,7) and (4.-3) in the
ratio 2 : 3.
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Answer 1

Answer:

SOLUTION:-

(x1,y1) is (-1,7)

(x2,y2) is (4,-3)

m1=2

m2=3

x = m1x2+m2x1/m1+m2

= (2×4)+(3×-1)/(2+3) = (8-3)/5

= 5/5 = 1

y = m1y2+m2y1/m1+m2

= (2×-3)+(3×7)/(2+3) = (-6+21)/5

= 15/5 = 3

So, the point is (1,3)

Step-by-step explanation:

Solution: -   A = (-1, 7) and B = (4, -3)

So, x 1 = − 1 ,

 y 1= 7 ,

 x 2 = 4  and  y 2=2 − 3

We also have;  

m 1 = 2  and  m 2 = 3

Let us assume P is the point of division

Coordinates of P can be calculated as follows by using section formula:

x = m 1 x 2 + m 2 x 1/ m 1 + m 2

= 2 × 4 + 3 × − 1 /5

= 8 − 3/ 5

= 5/ 5

= 1

 

y = m 1 y 2 + m 2 y 1 /m 1 + m 2

= 2 × − 3 + 3 × 7/ 5

= − 6 + 21 /5

= 15 /5

= 3

Hence, P = (1, 3)

Answer 2

Answer:

Let the coordinates of the point be P(x, y) which divides the line segment joining the points (-1, 7) and (4, - 3) in the ratio 2 : 3

Let two points be A (x₁, y₁) and B(x₂, y₂). P (x, y) divides internally the line joining A and B in the ratio m₁: m₂. Then, coordinates of P(x, y) is given by the section formula

P (x, y) = [(mx₂ + nx₁ / m + n), (my₂ + ny₁ / m + n)]

Find the coordinates of the point which divides the join of (-1, 7) and (4, - 3) in the ratio 2 : 3

Let x₁ = - 1, y₁ = 7, x₂ = 4 and y₂ = - 3, m = 2, n = 3

By Section formula, P (x, y) = [(mx₂ + nx₁ / m + n) , (my₂ + ny₁ / m + n)] --- (1)

By substituting the values in the equation (1)

x = [2 × 4 + 3 × (- 1)] / (2 + 3) and y = [2 × (- 3) + 3 × 7] / (2 + 3)

x = (8 - 3) / 5 and y = (- 6 + 21) / 5

x = 5/5 = 1 and y = 15/5 = 3

Therefore, the coordinates of point P are (1, 3).