Coordinate Geometry
Q1. Find a point on the yaxis equidistant from (− 5, 2) and (9, − 2).
Let the required point on the yaxis be P (0, y)
∴ PA = PB
⇒ y^{2} − y^{2} − 4y − 4y = 81 + 4 − 4 − 25
⇒ − 8y = 85 − 29
⇒ − 8y = 56⇒
∴ The required point is (0, −7).
Q2. Find a point on xaxis at a distance of 4 units from point A (2, 1).
Let the required point on xaxis be P (x, 0).
∴ PA = 4
⇒ x^{2} − 4x + 4 + 1 = 4^{2} = 16
⇒ x^{2} − 4x + 1 + 4 − 16 = 0
⇒ x^{2} − 4x − 11 = 0⇒
Q3. Find the distance of the point (3, − 4) from the origin.
The coordinates of origin (0, 0).
∴ Distance of (3, − 4) from the origin
Q4. For what value of x is the distance between the points A (− 3, 2) and B (x, 10) 10 units?
The distance between A (− 3, 2) and B (x, 10)
⇒ (x + 3)^{2} + (8)^{2} = 10^{2}
⇒ (x + 3)^{2} = 10^{2} − 8^{2}
⇒ (x + 3)^{2} = (10 − 8) (10 + 8) = 36
⇒
For +ve sign, x =6 − 3 = 3
For −ve sign, x = − 6 − 3 = − 9
Q5. Find a point on the xaxis which is equidistant from points A (5, 2) and B (1, − 2).
The given points are: A (5, 2) and B (1, − 2) Let the required point on the xaxis be C (x, 0).
Since, C is equidistant from A and B.
∴ AC = BC∴ 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).
As P is equidistant from A and B
∴ PA = PBwhich 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)
Since, P (x, y) is equidistant from A (−5, 3) and B (7, 2)
∴ AP = BP
Q8. 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
Coordinates of the mid point of BC are:
Coordinates of the mid point of AC are:
Q9. Find the distance between the points
Distance between is given by
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.
Here, P (6, b − 2) and Q (− 2, 4) are the given points.
∴ Mid point of PQ is given by:
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1. What is coordinate geometry? 
2. How are coordinates represented in coordinate geometry? 
3. What is the distance formula in coordinate geometry? 
4. How do you find the midpoint of a line segment in coordinate geometry? 
5. How do you determine if three points are collinear in coordinate geometry? 

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