What are the coordinates of point 1/4 of the way from A(-6,-3) to B(10,9)

Answer 1

Xend + 3*Xstart Yend + 3*Ystart

-------------------- ---------------------

4 4

10 + 3*-6 9 + 3*-3

------------ = -2 ----------- = 0

4 4

check:

THe whole distance is

sqrt( (-6 - 10)^2 + (-3 - 9)^2 )

= sqrt( (-16)^2 + (-12)^2 )

= sqrt( 256 + 144)

= sqrt(400)

= 20

1/4 of that is 5

Distance from (-6, -3) to (-2 ,0) is

sqrt( (-6- -2)^2 + (-3-0)^2)

= sqrt( (-4)^2 + (-3)^2 )

= sqrt ( 16 + 9)

= sqrt(25)

= 5

(-2,0) is correct

Answer 2

Starting from A, to get 1/4 of the way along line AB, you need to increase the x- and y-coordinates of A by 1/4 of the difference of the relevant coordinates of A and B, respectively.

Let's call the point we're looking for C. C_x = A_x + .25 (B_x - A_x) and C_y = A_y + .25 (B_y - A_y)

For these particular points. C_x = -6 + .25 (10 - (-6)) = -2 and C_y = -3 + .25 (9 - (-3)) = 0

So Point C is found at (-2, 0)

Answer 3