Question

A point H on a segment with endpoints B (3, -1) and Z (12, 5) partitions the segment in a 5:1 ratio. Find H. You must show all work to receive credit.

Answer 1

I thought I was supposed to multiply the distance between the x coordinates (9 in this case) by the ratio (5/1) but that ends up being 45, which seems like waay too much.. :/

Answer 2

@jdoe0001 do you know?

Answer 3

\(\bf B(3,-1)\qquad Z(12,5)\\ \quad \\ \quad \\

\color{blue}{\cfrac{ZH}{BH}=\cfrac{ratio1}{ratio2}\implies ratio2\cdot ZH=ratio1\cdot BH\quad \textit{dividing by H}\\ \quad \\
ratio2\cdot Z=ratio1\cdot B\implies} 5(12,5)=1(3,-1)\\ \quad \\\qquad \color{blue}{H=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}\\ \quad \\

\qquad thus\qquad \\ \quad \\
H=\left(\cfrac{(5\cdot 12)+(1\cdot 3)}{1+5}\quad ,\quad \cfrac{(5\cdot 5)+(1\cdot -1)}{1+5}\right)\)

Answer 4

Is there any way you could explain this to me in words? I'm trying to understand but it's a little confusing. Thanks for the answer, though.

Answer 5

is almost the same as doing similarity checks using proportions
if you have done similarity checks, then you can see that the ratios "ratio" is being equivaled to the 2 points given

Answer 6

http://www.teacherschoice.com.au/Maths_Library/Analytical%20Geometry/AnalGeom_3.htm <--- not sure if this helps

Answer 7

Thank you, you were very helpful. a lifesaver!