Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

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Class 10 : Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

The document Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev is a part of the Class 10 Course Class 10 Mathematics by VP Classes.
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Q1. Find a point on the y-axis equidistant from (− 5, 2) and (9, − 2).

Sol. Let the required point on the y-axis be P (0, y)

∴ PA = PB

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

⇒ y2 − y2 − 4y − 4y = 81 + 4 − 4 − 25
⇒ − 8y = 85 − 29
⇒ − 8y = 56

⇒  Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

∴ The required point is (0, −7).

Q2. Find a point on x-axis at a distance of 4 units from the point A (2, 1).

Sol. Let the required point on x-axis be P (x, 0).

∴ PA = 4

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev
⇒ x2 − 4x + 4 + 1 = 42 = 16
⇒ x2 − 4x + 1 + 4 − 16 = 0
⇒ x2 − 4x − 11 = 0

⇒  Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

Q3. Find the distance of the point (3, − 4) from the origin.

Sol. The coordinates of origin (0, 0).
∴ Distance of (3, − 4) from the origin

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

Q4. For what value of x is the distance between the points A (− 3, 2) and B (x, 10) 10 units?

Sol. The distance between A (− 3, 2) and B (x, 10)

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev
Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev
⇒ (x + 3)2 + (8)2 = 102
⇒ (x + 3)2 = 102 − 82
⇒ (x + 3)2 = (10 − 8) (10 + 8) = 36
⇒  Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev
For +ve sign, x =6 − 3 = 3
For −ve sign, x = − 6 − 3 = − 9

Q5. Find a point on the x-axis which is equidistant from the points A (5, 2) and B (1, − 2).
 Sol. 
The given points are: A (5, 2) and B (1, − 2) Let the required point on the x-axis be C (x, 0).
Since, C is equidistant from A and B.
∴ AC = BC

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

∴ The required point is (0, 3).
Q6. Establish the relation between x and y when P (x, y) is equidistant from the points A (− 1, 2) and B (2, − 1).

Sol. ∵ P is equidistant from A and B
∴ PA = PB

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

which is the required relation.

Q7. Find a relation between x and y such that the point P (x, y) is equidistant from the points A (−5, 3) and B (7, 2) 

Sol. Since, P (x, y) is equidistant from A (−5, 3) and B (7, 2)
∴ AP = BP

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

Q8. Show that the points (7, − 2), (2, 3) and (− 1, 6) are collinear.

Sol. Here, the vertices of a triangle are (7, − 2), (2, 3) and (− 1, 6)
∴ Area of the triangle

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

Since area of triangle =  0
∴ The vertices of the triangle are collinear.
Thus, the given points are collinear.

Q9. Find the distance between the points  Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

Sol. Distance between Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev  is given by

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

Q10. If the mid point of the line joining the points P (6, b − 2) and Q (− 2, 4) is (2, − 3), find the value of b.

Sol. Here, P (6, b − 2) and Q (− 2, 4) are the given points.
 ∴ Mid point of PQ is given by:

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev
Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

Q11. In the given figure, ABC is a triangle. D and E are the mid points of the sides BC and AC respectively. Find the length of DE. Prove that Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

Sol. Coordinates of the mid point of BC are:

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

Coordinates of the mid point of AC are:

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

Very Short Answer Type Questions- Coordinate Geometry Class 10 Notes | EduRev

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