Question

A point M on a segment with endpoints X (1, −2) and Y (10, 3) partitions the segment in a 4:1 ratio. Find M. You must show all work to receive credit.

Answer 1

I seriously have no clue how to do this, and ive been on it for the past hour

Answer 2

one sec

Answer 3

Okay!

Answer 4

see the points now? notice that a 4:1 ratio means
the point M splits the line in 5 pieces

Answer 5

see the ratio ?

Answer 6

I believe so yeah!

Answer 7

ok gimme one sec

Answer 8

Okay! Thank you so much btw

Answer 9

hmmm got a little bit truncated...lemme fix that

Answer 10

\(\bf \textit{internal division of a line segment}
\\ \quad \\

X(1,-2)\qquad Y(10,3)\qquad ratio1=4\qquad ratio2=1\qquad 4:1\\ \quad \\ \quad \\

\cfrac{X\cancel{ M }}{\cancel{ M }Y}=\cfrac{ratio1}{ratio2}
\\ \quad \\
\implies
ratio2\cdot X=ratio1\cdot Y\quad \implies 1(1,-2)=4(10,3)
\\ \quad \\

{\color{brown}{ M=\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 \\
M=\left(\cfrac{(1\cdot 1)+(4\cdot 10)}{4+1}\quad ,\quad \cfrac{(1\cdot -2)+(4\cdot 3)}{4+1}\right)\)

Answer 11

How would I write all that out a show it using all my work?

Answer 12

see above

Answer 13

Okay!