Question

If a line is extended from A (2,3) through B ( -2, 0 ) to a point so that AC = 4ab Find the coordinates of C

Please help thanks so much
GEOMETRY MIDPOINT FORMULA - Steve, Thursday, January 30, 2014 at 11:58am
B-A = (-4,-3)
C-A = 4(B-A) = (-16,-12)
C = A+(C-A) = (-14,-9)

Answer 1

looks like Steve was using vector geometry

Perhaps the following approach might make sense to you:

make a sketch.
since AC = 4AB
AB : BC = 1 : 3

for the x's :
(2 - (-2))/(-2-x) = 1/3
12 = -2-x
x = -14

for the y's:

(3-0)/(0-y) = 1/3
9 = -y
y = -9

so point C is (-14, -9)

Answer 2

thank you reinyyyyy <3

Answer 3

Sorry to be obscure, Joy. It was sort an informal shortcut, so I could present the subtraction of x- and y-values both at once. If you look carefully at Reiny's calculations, you will see that the same subtractions show up in my pairs of numbers.

The logic was: figure the differences in x and y going from A to B: B-A

Multiply those differences by 4

Add those scaled differences to the original values for A, and you get the values for C.

Answer 4

thankssssss steve :) <33

Answer 5

What formula did you use?

Answer 6

hello, how did you got the ratio AB : BC = 1:3 ? Im just a little confuse, please explain briefly with the fraction, thanks.