Question

Geometry question

Answer 1

If the point \(R(1,-2)\) divides externally the line segment joining \(P(2,5)\) and \(Q\) in the ratio \(3:4\) , what will be the co-ordinates of \(Q\)?

\(\large \color{black}{\begin{align} &a.)\ (-3,6)\hspace{.33em}\\~\\
&b.)\ (2,-4)\hspace{.33em}\\~\\
&c.)\ (3,6)\hspace{.33em}\\~\\
&d.)\ (1,2)\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

You're directly applying the formula for external division.

Answer 3

u mean this one


\(\large \color{black}{\begin{align}\ x=\dfrac{mx_2-nx_1}{m-n}\\\hspace{.33em}\\~\\
\end{align}}\)

Answer 4

Precisely.

Answer 5

but i m not getting the answer from the choices

Answer 6

Are you sure you chose your points and their values in the right order?

Answer 7

none of the options even lie on the given line segment PR

Answer 8

presuming you want a point Q such that R,P,Q are collinear

Answer 9

True, I'm getting something else.

Answer 10

easy way to convince and kill the question is by considering the slope RP

slope of RP = 7

it is necessary that any two points on the same line must have same slope
pick any of the options for Q and work the slope RQ
none match, so another bogus question

Answer 11

ok the book is bogus

Answer 12

Does your book give you the answer (3,6)? I'm kinda trying to see how they got to a wrong answer.

Answer 13

yes \((3,6)\) is given correct

Answer 14

interesting, how did u get (3,6) PK

Answer 15

They solved it like this:

Answer 16

\[1 = 3\cdot x - 4 \cdot 2 \Rightarrow x = 3\]\[-2 = 3\cdot y - 20 \Rightarrow y = 6\]It's evidently wrong.

Answer 17

They made a really common mistake. External division does tend to confuse.