Find the coordinates of the point three tenths of the way from A to B.

Question

the coordinates of b is (9,5)

the coordinates of a is (-4,-6)

Answer 1

Graphing the points creating a large triangle whose hypotenuse is a line of y=(13/11)x - 15.636

You create 2 similar triangles with the smaller hypotenuse being 0.3 times the length of the larger triangle.

Length of larger hypotenuse = SQRT[(9+4)^2 + (-6 -5)^2] = 17.03

0.3 x 17.03 = 5.11 is the length of the smaller hypotenuse.

So using the ratios of the similar triangles: (small triangle : large triangle)

For the y coordinate ratio:

5.11:17.03 = y:5 yields y=1.5

For the x coordinate ratio:

5.11:17.03 = x:9 yields x=2.7

So the coordinates of the point 0.3 of the length of the big hypotenuse is (2.7,1.5)

Answer 2

A to B for y-values is 11. 3/10 of 11 is 33/10=3.3 -6+3.3=-2.7

A to B for x-values is 13 3/10 of 13 is 39/10=3.9 -4+3.9=-0.1

The point 3/10 from A to B is (-0.1,-2.7)

The two points lie on the line (5+6)/(9+4)=11/13=(y+6)/(x+4) slope = slope

11x+44 = 13y+78 cross multiply

Plug in the point (-0.1,-2.7) or x=-0.1=-1/10 and y=-2.7=-27/10 to check the answer