Question

The line segment AB meets the coordinates axes in points A and B. If point P(3,6) divides AB in the ratio 2:3,then find the points A and B​

Answer 1

Answer:-

The coordinates are A(5, 0) and B(0, 15)

Explanation:-

Given:-

• A line segment AB meets the coordimates axes in points A and B.

• A point p divides the line segment in ratio 2 : 3 internally.

ToFind:-

• The coordinates of A and B.

Formula Used:-

Section Formula:-

$\\ \large\orange{\longrightarrow\boxed{\pink{\bf X = \dfrac{m_1x_2+m_2x_1}{m_1+m_1}.}}}$

And

$\\\large\orange{\longrightarrow\boxed{\pink{\bf Y = \dfrac{m_1y_2+m_2y_1}{m_1+m_1}.}}}$

Where,

• X and Y are x and y coordinates of the point which divides the line segment.

• $\tt m_1\:\:And\:\:m_2$ are the first and second numerical values of the ratio in which the point divides the line segment.

• $\tt x_1\:\:And\:\:x_2$ are x-coordinates of both the points joining the line segment.

• $\tt y_1\:\:And\:\:y_2$ are y-coordinates of the points joining the line segment.

Note:-

• In the qiestion it is given that the points A and B meets the coordinates axes which means that A meets at y-axis and B meets at x - axis.

• So let the coordinates of A be (x, 0) and B be (0, y).

So Here,

• X and Y = 3 and 6 respectively.

• $\tt m_1\:\:And\:\:m_2$ = 2 and 3 respectively.

• $\tt x_1\:\:And\:\:x_2$ = x and 0 respectively.

• $\tt y_1\:\:And\:\:y_2$ = 0 and y respectively.

Now,

By using section formula we get:-

$\\ \bf\mapsto X = \dfrac{m_1x_2+m_2x_1}{m_1+m_1}.$

$\\ \tt\mapsto 3 = \dfrac{2(0) + 3(x)}{2 + 3} .$

$\\ \tt\mapsto \frac{0 + 3x}{5} =3.$

$\\ \tt\mapsto3x = 15.$

$\\ \tt\mapsto x = \frac{15}{3} .$

$\\ \large\red{ \mapsto \boxed{ \blue{ \bf x = 5.}}}$

Therefore The value of x is 3.

Similarly,

$\\ \bf\mapsto Y = \dfrac{m_1y_2+m_2y_1}{m_1+m_1}.$

$\\ \tt\mapsto 6 = \dfrac{2(y) + 3(0)}{2 + 3} .$

$\\ \tt\mapsto \frac{2y + 0}{5} = 6.$

$\\ \tt\mapsto2y = 30.$

$\\ \tt\mapsto y = \frac{30}{2}.$

$\\ \large\red{ \mapsto \boxed{ \blue{ \bf y = 15.}}}$

Therefore the value of y is 15.

Therefore,

• Coordinates of A = (x,0) = (5,0).

• Coordinates of B = (0, y) = (0, 15).

Answer 2

✭✭Answer:-✭✭


✭✭The coordinates are A(5, 0) and B(0, 15)


✭✭Explanation:-✭✭


✭Given:-

✰A line segment AB meets the coordimates axes in points A and B.


✰A point p divides the line segment in ratio 2 : 3 internally.


✭✭ToFind:-


✰The coordinates of A and B.


✭Formula Used:-


✰Section Formula:-


✰X=m1​+m1​m1​x2​+m2​x1​​.​​


✰And


✰⟶Y=m1​+m1​m1​y2​+m2​y1​​.​​


✰Where,


✰X and Y are x and y coordinates of the point which divides the line segment.


✰ m_2m1​Andm2​ are the first and second numerical values of the ratio in which the point divides the line segment.


✰x_2x1​Andx2​ are x-coordinates of both the points joining the line segment.


✰y_2y1​Andy2​ are y-coordinates of the points joining the line segment.



✭✭Note:-

✰In the qiestion it is given that the points A and B meets the coordinates axes which means that A meets at y-axis and B meets at x - axis.


✰So let the coordinates of A be (x, 0) and B be (0, y).


✭✭So Here,



✰X and Y = 3 and 6 respectively.


✰m_2m1​Andm2​ = 2 and 3 respectively.


✰x_2x1​Andx2​ = x and 0 respectively.


✰y_2y1​Andy2​ = 0 and y respectively.

✭✭Now,



✰✰By using section formula we get:-

✰↦X=m1​+m1​m1​x2​+m2​x1​​.​


✰↦3=2+32(0)+3(x)​.​


✰↦50+3x​=3.​


✰↦3x=15.​


✰↦x=315​.​


✰↦x=3.​​


✭✭Therefore The value of x is 3.


❖Similarly,❖


✰↦Y=m1​+m1​m1​y2​+m2​y1​​.​


✰↦6=2+32(y)+3(0)​.​


✰↦52y+0​=6.​


✰↦2y=30.​


✰↦y=230​.​


✰↦y=15.​​


❖❖Therefore the value of y is 15.


❖Therefore,❖

✿Coordinates of A = (x,0) = (5,0).


✿Coordinates of B = (0, y) = (0, 15).




✼✼ᴀክຟᗯᴇʳ..✼✼
✪✪✪.ⁱᵗᶻ ˢʰⁱʷᵃᵐ............✪✪✰




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