Find the coordinates of the point 3/10 of the way from A to B.

Question

A = (-3,-8)

B = (11,7)

Answer 1

Let's call the point 3/10 of the way between A and B point C. Point C has coordinates (x_C,y_C) as follows:

x_C = x_A + (3/10)(x_B-x_A)

y_C = y_A + (3/10)(y_B-y_A)

Plug in the numbers and compute the answers.

Answer 2

The point is 3/10 from A and 7/10 from B so use this method, which is basically a weighted average of the two endpoints.

M = 7/10 * A + 3/10 * B

Notices that the 7/10 is multiplied by A even though the point is 3/10 away from A and similarly 3/10 is multiplied by B even though the point is 7/10 away from B

Now we'll plug in

M = 7/10 * (-3, -8) + 3/10 * (11, 7)

The x-coordinate is 7/10 * (-3) + 3/10 * 11 = -21/10 + 33/10 = 12/10 = 1.2

The y-coordinate is 7/10 * (-8) + 3/10 * 7 = -56/10 + 21/10 = -35/10 = -3.5

Thus the point M is (1.2, -3.5)