Download App

Coordinate Geometry — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsCoordinate Geometry4 Marks
Question
To conduct Sports Day activities, in your rectangular-shaped school ground $ABCD,$ lines have been drawn with chalk powder at a distance of $1m$ each. $100$ flower pots have been placed at a distance of $1m$ from each other along $AD,$ as shown in Figure. Niharika runs $\frac{1}{4}$th the distance $AD$ on the $2nd$ line and posts a green flag. Preet runs $\frac{1}{5}$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$?$
✓

Answer

It can be observed that Niharika posted the green flag at $\frac{1}{4}$th of the distance $AD$ i.e., $\frac{1}{4} \times 100 = 25m$ from the starting point of $2^{nd}$ line. Therefore, the coordinates of this point $G$ is $(2, 25)$
Similarly, Preet posted a red flag at $\frac{1}{5}$th of the distance $AD$ i.e., $\frac{1}{5} \times 100 = 20m$ from the starting point of $8^{th}$ line. Therefore, the coordinates of this point $R$ are $(8, 20)$
Now we have the positions of posts by Preet and Niharika
According to distance formula, the distance between points $A(x_1, y_1)$ and $B(x_2, y_2)$ is given by
$D=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$
Distance between these flags by using distance formula,
$D=\sqrt{\left(8-2_{}\right)^{2}+\left(25_{}-{20}\right)^{2}}$
$=\sqrt{36+25} \mathrm {m}$
$=\sqrt{61} \mathrm{m}$
The point at which Rashmi should post her blue flag is the mid-point of the line joining these points. Let this point be $A (X,Y)$
Now by midpoint formula,
$(X, Y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$
$X=\left(\frac{2+8}{2}\right)=5$
$Y=\left(\frac{25+20}{2}\right)=22.5$
Hence,$ A (X,Y) = (5, 22.5)$
Therefore, Rashmi should post her blue flag at $22.5m$ on the $5^{th}$ line.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from Coordinate Geometry→Coordinate Geometry — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

In an $AP$, the first term is $-4$, the last term is $29$ and the sum of all its terms is $150$. Find the common difference.
→
Write the condition to be satisfied for which equations $ax^2+ 2bx + c = 0$ and $\text{bx}^2-2\sqrt{\text{ac}}\text{x}+\text{b}=0$ have equal roots.
→
In an equilateral triangle with side a, prove that area $=\frac{\sqrt{3}}{4}\text{a}^2.$
→
Prove the following identities:
$\sqrt{\frac{1+\sin\theta}{1-\sin\theta}}=(\sec\theta+\tan\theta)$
→
Solve the following system of linear equations graphically:
$3x + y - 11 = 0,$
$x - y - 1 = 0.$
Shade the region bounded by these lines and $y-$axis. Also, find the area of the region bounded by these lines and $y-$axis.
→
If $\frac{4}{5},\text{a},2$ are in $AP$, find the value of a.
→
In a cyclic quadrilateral $ABCD$ $\angle\text{A}=(2\text{x}+4)^\circ,\angle\text{B}=(\text{y}+3)^\circ,$ $\angle\text{C}=(2\text{y}+10)^\circ,\angle\text{D}=(4\text{x}-5)^\circ.$ Find the four angles.
→
The sum of two natural numbers is $15$ and the sum of their reciprocals is $\frac{3}{10}.$ Find the numbers.
→
In the figures given below, an altitude is drawn to the hypotenuse by a right-angled triangle. The length of different line-segment are marked in figure. Determine$ x, y, z$ in case.
→
Prove the following trigonometric identities.
$\frac{1-\cos\text{A}}{1+\cos\text{A}}=(\cot\text{A}-\text{cosec A})^2$
→