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Coordinate Geometry

The document contains a series of coordinate geometry problems, including calculations of distances, areas, and properties of geometric figures such as triangles and rectangles. It presents multiple-choice questions with specific coordinates and asks for various geometric properties or relationships. The problems cover topics such as midpoints, diagonals, and collinearity, providing a comprehensive overview of coordinate geometry concepts.

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dhruvavnair
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23 views2 pages

Coordinate Geometry

The document contains a series of coordinate geometry problems, including calculations of distances, areas, and properties of geometric figures such as triangles and rectangles. It presents multiple-choice questions with specific coordinates and asks for various geometric properties or relationships. The problems cover topics such as midpoints, diagonals, and collinearity, providing a comprehensive overview of coordinate geometry concepts.

Uploaded by

dhruvavnair
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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COORDINATE GEOMETRY

1. The distance of the point P (2, 3) from the x-axis is


(A) 2 (B) 3 (C) 1 (D) 5
2. The distance between the points A (0, 6) and B (0, –2) is
(A) 6 (B) 8 (C) 4 (D) 2
3. The distance of the point P (–6, 8) from the origin is
(A) 8 (B) 2√7 (C) 10 (D) 6
4. The distance between the points (0, 5) and (–5, 0) is
(A) 5 (B) 5√2 (C) 2√5 (D) 10
5. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and
B (5, 0). The length of its diagonal is
(A) 5 (B) 3 (C) √34 (D) 4
6. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(A) 5 (B) 12 (C) 11 (D) 7+√5
7. The area of a triangle with vertices A (3, 0), B (7, 0) and C (8, 4) is
(A) 14 (B) 28 (C) 8 (D) 6
8. The points (–4, 0), (4, 0), (0, 3) are the vertices of a
(A) right triangle (B) isosceles triangle
(C) equilateral triangle (D) scalene triangle
9. The point which divides the line segment joining the points (7, –6) and (3, 4)
in ratio 1 : 2 internally lies in the
(A) I quadrant (B) II quadrant
(C) III quadrant (D) IV quadrant
10. The point which lies on the perpendicular bisector of the line segment joining
the points A (–2, –5) and B (2, 5) is
(A) (0, 0) (B) (0, 2) (C) (2, 0) (D) (–2, 0)
11. The fourth vertex D of a parallelogram ABCD whose three vertices are A (–
2, 3), B (6, 7) and C (8, 3) is
(A) (0, 1) (B) (0, –1) (C) (–1, 0) (D) (1, 0)
12. If the point P (2, 1) lies on the line segment joining points A (4, 2) and B (8,
4), then
1
(A) AP = AB (B) AP = PB (C) PB
3
1 1
= AB (D) AP = AB
3 2
𝑎
13. If P ( , 4 ) is the mid-point of the line segment joining the points Q (– 6, 5)
3

and R (– 2, 3), then the value of a is


(A) – 4 (B) – 12 (C) 12 (D) – 6
14. The perpendicular bisector of the line segment joining the points A (1, 5) and
B (4, 6) cuts the y-axis at
(A) (0, 13) (B) (0, –13)
(C) (0, 12) (D) (13, 0)
15. The coordinates of the point which is
equidistant from the three vertices of the Δ
AOB as shown in the Fig.
(A) (𝑥, 𝑦) (B) (𝑦, 𝑥)
𝑥 𝑦 𝑦 𝑥
(C) ( , ) (D) ( , )
2 2 2 2

16. A circle drawn with origin as the centre


13
passes through ( ,0). The point which does
2

not lie in the interior of the circle is


3 7 1 5
(A) (– , 1 ) (B) ( 2, ) (C) ( 5, − ) (D) (−6, )
4 3 2 2

17. A line intersects the y-axis and x-axis at the points P and Q, respectively. If
(2, –5) is the mid-point of PQ, then the coordinates of P and Q are,
respectively
(A) (0, – 5) and (2, 0) (B) (0, 10) and (– 4, 0)
(C) (0, 4) and (– 10, 0) (D) (0, – 10) and (4, 0)
18. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is
(A) 4 only (B) ± 4 (C) – 4 only (D) 0
19. If the points A (1, 2), O (0, 0) and C (a, b) are collinear, then
(A) a = b (B) a = 2b
(C) 2a = b (D) a = –b
20. If the mid-point of the line segment joining the points A (3, 4) and
𝐵 (𝑘, 6) 𝑖𝑠 𝑃 (𝑥, 𝑦) and 𝑥 + 𝑦 – 10 = 0, find the value of k.

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