Question

J has coordinates (-2,8) R has coordinates (-7,-3) find the coordinates of point A that partition (JR) in the ratio 5:2 and sketch points J,A,R, and (JA) on the coordinate plane below.

Answer 1

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.