Question
Find the ratio in which the line segment joining the points A(3,8) and B(-9, 3)is divided by the Y-axis.
✓
Answer
A point P(x,y) divides the line formed by points (a,b) and (c,d) in the ratio of m:n, then the coordinates of the point P is given by
$x =\frac{ an + cm }{ m + n } \text { and } y =\frac{ bn + dm }{ m + n }$
On y axis x coordinate = 0
Let the y-axis divide AB is ratio 1:k.
the points A(3,8) and B(-9, 3)is divided by the Y-axis.
For x coordinate
$0=\frac{3 k -9}{ k +1}$
Solving for k we get
3k - 9 = 0
3 k = 9
k = 3
Hence the y axis divides the given point in the ratio 3:1
$x =\frac{ an + cm }{ m + n } \text { and } y =\frac{ bn + dm }{ m + n }$
On y axis x coordinate = 0
Let the y-axis divide AB is ratio 1:k.
the points A(3,8) and B(-9, 3)is divided by the Y-axis.
For x coordinate
$0=\frac{3 k -9}{ k +1}$
Solving for k we get
3k - 9 = 0
3 k = 9
k = 3
Hence the y axis divides the given point in the ratio 3:1
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
→→→→→
Draw a circle of radius 4.2 cm, take any point M on it. Draw tangent to the circle from point M
Prove the following identites:
$\frac{1}{\big(1+\tan^2\theta\big)}+\frac{1}{\big(1+\cot^2\theta\big)}=1$
→$\frac{1}{\big(1+\tan^2\theta\big)}+\frac{1}{\big(1+\cot^2\theta\big)}=1$
Which of the following are quadratic equations?
$x^2 - 3x = 0$
→$x^2 - 3x = 0$
The $24^{\text {th }}$ term of an AP is twice its $10^{\text {th }}$ term. Show that its $72^{\text {nd }}$ term is 4 times its $15^{\text {th }}$ term.
→In the figure, there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5cm, find the
lengths of PS.
lengths of PS.
Write the lower limit of the modal class of the following frequency distribution?
|
Age (in years)
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
50-60
|
|
Number of patients
|
16
|
13
|
6
|
11
|
27
|
18
|
Solve the following quadratic equation by completing square method:
$3 y^2+7 y+1=0$
→$3 y^2+7 y+1=0$
The points $A \left( x _1, y _1\right), B \left( x _2, y _2\right)$ and $C \left( x _3, y _3\right)$ are the vertices of $\triangle A B C$.
What are the coordinates of the centroid of the triangle $A B C$ ?
→What are the coordinates of the centroid of the triangle $A B C$ ?