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Coordinate Geometry
CBSE 2026 Board Exam Set 1 (Code 30/1/1)
CBSE_BOARD_PYQ_2026_30_1_1
Grade 10
Question:
[Section E]
Case Study 2: Sports Day Activity
To conduct Sports Day activities in a 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 $AD$. Niharika runs $1/4^{\text{th}}$ the distance $AD$ on the $2^{\text{nd}}$ line and posts a green flag at point $G$. Preet runs $1/5^{\text{th}}$ the distance $AD$ on the $8^{\text{th}}$ line and posts a red flag at point $R$.
1. Write the coordinates of Green flag $G$ and Red flag $R$. (1 Mark)
2. Find the distance between both the flags ($GR$). (1 Mark)
3. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, at what distance and on which line should she post her flag? (2 Marks)
OR (for part 3)
3. If Joy has to post a yellow flag at a point $K$ on the line segment $GR$ such that $GK : KR = 1 : 2$, find the coordinates of point $K$. (2 Marks)
Case Study 2: Sports Day Activity
To conduct Sports Day activities in a 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 $AD$. Niharika runs $1/4^{\text{th}}$ the distance $AD$ on the $2^{\text{nd}}$ line and posts a green flag at point $G$. Preet runs $1/5^{\text{th}}$ the distance $AD$ on the $8^{\text{th}}$ line and posts a red flag at point $R$.
1. Write the coordinates of Green flag $G$ and Red flag $R$. (1 Mark)
2. Find the distance between both the flags ($GR$). (1 Mark)
3. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, at what distance and on which line should she post her flag? (2 Marks)
OR (for part 3)
3. If Joy has to post a yellow flag at a point $K$ on the line segment $GR$ such that $GK : KR = 1 : 2$, find the coordinates of point $K$. (2 Marks)
Step-by-Step Solution
Key Concept: $G(2, 25)$ and $R(8, 20)$.
1. $G(2, 25)$ and $R(8, 20)$. [1.0 Mark]
2. Distance $GR = \sqrt{6^2 + (-5)^2} = \sqrt{61}$ m. [1.0 Mark]
[Part 3 Main] Midpoint $M = (5, 22.5)$. Post on $5^{\text{th}}$ line at $22.5$ m. [2.0 Marks]
-------------------------------
[Part 3 OR Choice]
$K = (4, 70/3)$. [2.0 Marks]
2. Distance $GR = \sqrt{6^2 + (-5)^2} = \sqrt{61}$ m. [1.0 Mark]
[Part 3 Main] Midpoint $M = (5, 22.5)$. Post on $5^{\text{th}}$ line at $22.5$ m. [2.0 Marks]
-------------------------------
[Part 3 OR Choice]
$K = (4, 70/3)$. [2.0 Marks]
Correct Answer: 1. G(2, 25), R(8, 20), 2. \sqrt{61} m, 3. 5th line at 22.5 m (OR K(4, 70/3))
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