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J Coordinates: (-2,8)
R Coordinates: (-7,-3)
A cuts JR in the ratio of 5:2
We have to find out the coordinates for A. Let coordinates of A be (x,y)
The section formula helps us determine a point (x,y) that divides the line joining two points (x1,y1) and (x2,y2) in the ratio of m:n
x1, y1 represents the point which is more on the left side of the x axis, while x2,y2 represents the point which is more on the right side of the x axis
So here x1 = -7, y1 = -3, x2 = -2, y2 = 8, m = 5, n = 2
As per section formula, x = (mx₂ + nx₁) / (m + n), and y = (my ₂ + ny₁) / (m + n))
⇒ x = ((5*-2) + (2*-7)) / (7)
⇒ x = (-10+ (-14)) / (7)
⇒ x = -24 / 7
⇒ x = -3.43
and y = ((5*8) + (2*-3)) / (7)
⇒ y = (40 - 6) / 7
⇒ y = 4.86
So coordinates of A are (-3.43,4.86)
Please see the attached image for seeing the points and line on chart.
