Question

Find the ratio in which the line segment joining the points (-4,12), and(7,-9) is divided by (-2,7) .​

Answer 1

Given point

P( - 4 , 12 ) and Q(7 , -9)

Line Segment Divided by R(-2 , 7)

To find

Ratio in which line segment Divided

Formula

x = (mx₂ + nx₁)/(m + n) and y = (my₂ + ny₁)/(m + n)

We Have

x = - 2 , y = 7 , x₁ = -4 , y₁ = 12 , x₂ = 7 and y₂ = -9

Let

the ratio , p:1 , we get p = m and n = 1

Put the value on formula

-2 = (7p - 1(4))/(p + 1)

-2 = (7p - 4)/(p + 1)

-2( p + 1) = 7p - 4

-2p - 2 = 7p - 4

-2p - 7p = -4+2

-9p = -2

p = 2/9

Now we have

p:1

where p = 2/9

2/9:1

2:9

we get ratio 2:9

Answer

Ratio is 2:9

Answer 2

Answer:

Given :-

• The line segment joining the points (- 4 , 12) , and (7 , - 9) is divided by (- 2 , 7).

To Find :-

• What is the ratio in which the line segment joining the points (- 4 , 12) and (7 , - 9) is divided by (- 2 , 7).

Formula Used :-

$\clubsuit$ Section Formula :

$\longmapsto \sf\boxed{\bold{\pink{x =\: \bigg(\dfrac{m_1x_2 + m_2x_1}{m_1 + m_2}\bigg)}}}$

Solution :-

Let, the ratio be k : 1

Then,

• m₁ = k
• m₂ = 1

Given points :

$\mapsto$ A(- 4 , 12)

$\mapsto$ B(7 , - 9)

And, points C(- 2 , 7) divide A and B.

So we get,

• x₁ = - 4
• y₁ = 12
• x = - 2
• x₂ = 7
• y₂ = - 9
• y = 7

According to the question by using the formula we get,

$\implies \sf - 2 =\: \bigg(\dfrac{k \times 7 + 1 \times (- 4)}{k + 1}\bigg)$

$\implies \sf - 2 =\: \bigg(\dfrac{7k + (- 4)}{k + 1}\bigg)$

$\implies \sf - 2 =\: \bigg(\dfrac{7k - 4}{k + 1}\bigg)$

By doing cross multiplication we get,

$\implies \sf - 2(k + 1) =\: 7k - 4$

$\implies \sf - 2k - 2 =\: 7k - 4$

$\implies \sf - 2k - 7k =\: - 4 + 2$

$\implies \sf {\cancel{-}} 9k =\: {\cancel{-}} 2$

$\implies \sf 9k =\: 2$

$\implies \sf k =\: \dfrac{2}{9}$

Hence, the ratio is k : 1 so,

$\leadsto \sf k : 1$

$\leadsto \sf \dfrac{2}{9} : 1$

$\leadsto \sf\bold{\red{2 : 9}}$

$\therefore$ The ratio in which the line segment joining the points b(- 4 , 12) and (7 , - 9) is divided by (- 2 , 7) is 2 : 9.