Question

Line segment JK in the coordinate plane has endpoints with coordinates (-4,11) and (8,-1). Which coordinates for point M divide bar (JK) into two parts so that the lengths of bar (JM) and bar (MK) are in a ratio of 1:3?

Answer 1

The coordinates for point M that divide the line segment JK with endpoints (-4,11) and (8,-1) into a 1:3 ratio are (-1,8) using the section formula.

Step-by-step explanation:

To find the coordinates for point M that divide the line segment JK in the ratio 1:3, we can use the section formula. Given that J has coordinates (-4,11) and K has coordinates (8,-1), and the ratio is 1:3, we apply the section formula for internal division:

1. Calculate the weighted average of the x-coordinates: Mx = [(1*8) + (3*(-4))] / (1+3) = (8 - 12) / 4 = -4 / 4 = -1.
2. Calculate the weighted average of the y-coordinates: My = [(1*(-1)) + (3*11)] / (1+3) = (-1 + 33) / 4 = 32 / 4 = 8.

Therefore, the coordinates for point M that divide the line segment JK into two parts such that the lengths of JM and MK are in a ratio of 1:3 are (-1,8).