Find the coordinates of the point 3/10 of the way from A to B. a=(-4,-5) b=(11,6)

Answer 1

change in x coordinates is 11-(-4)=15 3/10 of 15 is 4.5 -4+4.5= 0.5, the x-coordinate of 3/10 of the way from A to B.

change in y coordinates is 6-(-5)=11. 3/10 of 11 is 33/10 = 3.3. 3.3+(-5)= -1.7

the point 3/10 of the way from A to B is (0.5, -1.7)

It may help to draw a sketch on a graph and see if the point looks about right, It does.

Or derive the slope and equation for the line that runs through A to B. slope is rise over run, or 11/15

then use the point slope formula to derive the lines' equation: y-6=(11/15)(x-11)

15y-90=11x-121

15y-11x=-31

Now plug in the point (0.5,-1.7) into that equation

15(-1.7)-11(.5)=-31

25.5-5.5=-31

-31=-31

It works. That point is on the line connecting A to B

-18.7 -7.5 = -.99

Answer 2

Draw on graph paper a right triangle which these coordinates describe. From -4,-5 draw a horizontal line until you are directly under (11,6) (which is (11,-5), then draw a vertical line from (11,-5) to (11,6). The hypotenuse goes directly from (-4,-5) to (11,6), which lies right on top the coordinates you are trying to find.

The coordinates on the hypotenuse have corresponding coordinates on the x- and y- axis, so if you move 3/10ths of the way from A to B, you are also moving 3/10ths of the way along the x- and y- axis. Can you solve it from here?

Answer 3

Vector AB = <11 - (-4), 6 - (-5)> = <15, 11>. Let point C(x, y) devided distance from A to B as 3/10.

So AC = 3/13AB; <x + 4, y + 5> 3/13<15, 11>; x + 4 = 45/13; x = - 7/13; y+ 5 = 33/13, y = - 32/13.

So point C(- 7/13, - 32/13)