Question

SOLVE QUESTION 3 and 4


ANSWER BY MATHS AARYABHAT AND MATHS EXPERT​

Answer 1

1. QuestioN :

To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in figure. 7.12

Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

Given :

• ABCD is a rectangular shaped school ground.
• And, Lines have been drawn with chalk powder at a distance of 1m each.
• 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in figure. 7.12

Now,

$\tt \longrightarrow AD = 1 \times 100 m = 100m.$

A/Q,

• Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag.

$\tt \longrightarrow \dfrac{1}{4} \times 100 = 25m.$

distance cover by Niharika is 25m.

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• Preet runs 1/5 th the distance AD on the eighth line and posts a red flag.

$\tt \longrightarrow\dfrac{1}{5} \times 100 = 20m.$

distance cover by Preet is 20m.

Now,

• According to coordinate let,
• Niharika ( 2 , 25 ) = Q
• Preet ( 8 , 20 ) = R

$\tt \longrightarrow QR = \sqrt{(X_2 - X_1)^2 + ( y_2 - y1 )^2}$

$\tt \longrightarrow QR = \sqrt{(8 - 2)^2 + ( 20- 25)^2}$

$\tt \longrightarrow QR = \sqrt{36+ 25}$

$\tt \longrightarrow QR = \sqrt{61} \: m .$

So, the distance between both the flags is √61 m.

______________________________

• If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags.

Apply mid - point formula.

$\tt \longrightarrow \bigg( \dfrac{X_1 + X_2}{2} , \dfrac{y_1+ y_2}{2}\bigg)$

$\tt \longrightarrow \bigg( \dfrac{2 + 8}{2} , \dfrac{25 + 20}{2}\bigg)$

$\tt \longrightarrow \bigg( 5 \: , \: \dfrac{45}{2}\bigg)$

coordinate where should she post her flag is ( 5 , 45/2 )

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2. QuestioN :

Find the ratio in which the line segment joining the points (- 3 , 10 ) and ( 6 , - 8 ) is divided bу ( - 1, 6 ).

Apply section formula.

where as,

• A = ( - 3 , 10 )
• B = ( 6 , - 8 )
• P = ( - 1 , 6 )
• M , N the line segment joining the points AB.
• P is a point where AB line divided.

$\tt \longrightarrow \bigg( \dfrac{MX_2 + NX_1}{M+ N} + \dfrac{My_2 + Ny_1}{M+ N}\bigg)$

$\tt \longrightarrow \dfrac{6M+ ( - 3)N}{M+ N} = - 1$

$\tt \longrightarrow 6M+ ( - 3)N = - M - N$

$\tt \longrightarrow 7M= 2 N$

$\tt \longrightarrow \frac{M}{N}= \frac{2}{7}$

therefore, required ratio is 2 : 7.

Answer 2

Step-by-step explanation:

ANSWER NO 3.

From the given figure, the position of green flag posted by Niharika is $\tt M\left(2 \times 1, \dfrac{1}{4} \times 100\right)$

i.e. M(2,25) and red flag posted by Preet is $\tt N\left(8 \times 1, \dfrac{1}{5} \times 100\right)$ i.e. N(8,20) .

Now, $\tt M N=\sqrt{(8-2)^{2}+(20-25)^{2}}$

$\color{maroon}\[ \begin{array}{r} \tt {\left[\because \text { distance }=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}\right]} \\ \\ \tt =\sqrt{(6)^{2}+(-5)^{2}}=\sqrt{36+25}=\sqrt{61} \end{array} \]$

Hence, the distance between flags is $\tt \sqrt{61} m$.

Let P be the position of the blue flag posted by Rashmi in the half way of line segment MN .

Then, coordinates of

$\color{purple}\begin{aligned} \tt P & \tt=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right) \\ \\ & \tt=\left(\frac{2+8}{2}, \frac{25+20}{2}\right) \\ \\ & \tt=\left(\frac{10}{2}, \frac{45}{2}\right) \\ \\ & \tt=(5,22.5) \end{aligned}$

Hence, the blue flag is on the 5 th line at a distance of 22.5 m above it.