3 years ago

What is the value of x?X=?

Mathematics

1 answer:

Free_Kalibri [48]3 years ago

7 0

The answer of x is 54

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CD has the endpoints C(3, 2) and D(–5, –2). Charlie wants to place the point E at the point that partitions this line segment in

Ganezh [65]

So ... notice the picture below... the ratio is 3:1 from C to D, meaning the segment CE takes 3 units, whilst the ED segment takes 1

anyhow

$\bf \textit{internal division of a line segment}
\\ \quad \\\\
C(3,2)\qquad D(-5,-2)\qquad
ratio1=3\qquad ratio2=1\qquad 3:1
\\\\\\
\cfrac{C\underline{ E }}{\underline{ E }D}=\cfrac{ratio1}{ratio2}\implies 
ratio2\cdot C=ratio1\cdot D
\\\\\\
1(3,2)=3(-5,-2)
\\ \quad \\\\
{{ E=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}}$

$\bf \qquad thus
\\\\\\
E=\left(\cfrac{(1\cdot 3)+(3\cdot -5)}{3+1}\quad ,\quad \cfrac{(1\cdot 2)+(3\cdot -2)}{3+1}\right)$