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

To solve our given problem we will use section formula :]

Section Formula states that, when a point divides a line segment internally in the ratio m:n, So the coordinates are :]

Let

(-1 , 7) = (x₁ , y₁)

(4 , -3) = (x₂ , y₂)

m = 2

n = 3

The coordinates of the point in question is (1, 3).

Step-by-step explanation:

Point (-1, 7) is above and to the left of the point (4, -3). The point in question is to the right and below the point (-1, 7).

What will be the horizontal distance between the point (-1, 7) and the point in question?

The horizontal distance between the point (-1, 7) and (4, -3) is 5. Let the horizontal distance between the point (-1, 7) and the point in question be . Let the horizontal distance between the point in question and point (4, -3) be .  

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However,

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In other words, the point in question is 2 units to the right of the point (-1, 7). The x-coordinate of this point shall be .

The vertical distance between the point (-1, 7) and the point (4, -3) is 10. Similarly, the point in question is units below the point (-1, 7). The y-coordinate of this point will be .

Thus, the point in question is (1, 3).