Question
The line segment joining A $(4, 7)$ and B $(-6, -2)$ is intercepted by the y – axis at the point K. write down the abscissa of the point K. hence, find the ratio in which K divides AB. Also, find the co-ordinates of the point K.
✓
Answer
Since, point K lies on y-axis, its abscissa is $0.$
Let the point K $(0, y)$ divides AB in the ratio $k : 1$
We have,
$x=\frac{k \times(-6)+1 \times 4}{k+1} $
$ 0=\frac{-6 k+4}{k+1} $
$ k=\frac{4}{6}=\frac{2}{3}$
Thus, K divides AB in the ratio $2: 3.$
Also, we have:
$y=\frac{k \times(-2)+1 \times 7}{k+1} $
$y=\frac{-2 k+7}{k+1}$
$ y=\frac{-2 \times \frac{2}{3}+7}{\frac{2}{3}+1}$
$ y=\frac{-4+21}{2+3} $
$y=\frac{17}{5}$
Thus, the co-ordinates of the point K are $\left(0, \frac{17}{5}\right)$
Let the point K $(0, y)$ divides AB in the ratio $k : 1$
We have,
$x=\frac{k \times(-6)+1 \times 4}{k+1} $
$ 0=\frac{-6 k+4}{k+1} $
$ k=\frac{4}{6}=\frac{2}{3}$
Thus, K divides AB in the ratio $2: 3.$
Also, we have:
$y=\frac{k \times(-2)+1 \times 7}{k+1} $
$y=\frac{-2 k+7}{k+1}$
$ y=\frac{-2 \times \frac{2}{3}+7}{\frac{2}{3}+1}$
$ y=\frac{-4+21}{2+3} $
$y=\frac{17}{5}$
Thus, the co-ordinates of the point K are $\left(0, \frac{17}{5}\right)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream
If $15(2x^2 – y^2) = 7xy,$ find $x: y;$ if $x$ and $y$ both are positive.
→Calculate the amount and the compound interest for the following:
$Rs.12,500$ for $3$ years if the rates for the successive years are $8\%, 9\%$ and $10\%$ respectively.
→$Rs.12,500$ for $3$ years if the rates for the successive years are $8\%, 9\%$ and $10\%$ respectively.
Solve : $(x^2 – x)^2 + 5(x^2 – x)+ 4=0$
→ABC is a triangle. PQ is a line segment intersecting AB in P and AC in Q such that PQ ∥ BC and divides triangle ABC into two parts equal in area. Find the value of ratio BP : AB.
A polynomial $f(x)v when divided by $(x - 1)$ leaves a remainder $3$ and when divided by $(x - 2)$ leaves a remainder of $1.$ Show that when its divided by $(x - i)(x - 2),$ the remainder is $(-2x + 5).$
→In following fig., ABC is a right- angled triangle at A with sides $AB = 5 cm$ and $BC = 13 cm$ . A circle with centre $O$ has been inscribed in the triangle $ABC$. Calculate the radius of the incircle.
→How many two-digit numbers are divisible by 3?
Find the value of
$\frac{x+\sqrt{3}}{x-\sqrt{3}}+\frac{x+\sqrt{2}}{x-\sqrt{2}}$, if $\quad x=\frac{2 \sqrt{6}}{\sqrt{3}+\sqrt{2}}$.
→$\frac{x+\sqrt{3}}{x-\sqrt{3}}+\frac{x+\sqrt{2}}{x-\sqrt{2}}$, if $\quad x=\frac{2 \sqrt{6}}{\sqrt{3}+\sqrt{2}}$.
The radius of a sphere is $9$ cm. It is melted and drawn into a wire of diameter $2$ mm. Find the length of the wire in metre.
→