Question 1
Question: Find the distance between the following pair of points.[2 Mark]
(i) (-5, 3), (3, 1)
(ii) (4, 5), (-3, 2)
Answer: (i) Let A (x1, y1) = (-5, 3)
B (x2, y2) = (3, 1)
The distance between the points is

(ii) A = (4, 5) and B = (-3, 2)
Let (x1, y1) = (4,5) and (x2, y2) = (-3, 2)
The distance between the points is
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Question 2
Question: Find the distance between the following pairs of points.[Each 2 Marks]
(a) (-a, b) and (a, b)

Answer: (a) (x1, y1) = (-a, b) (x2, y2) = (a, b)
The distance between the two points is
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Distance between the two points is
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Distance between the two points is


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Distance between the two points is
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Question 3
Question: Use distance formula, show that the points (8, 7), (6, 4) and (0, -5) are collinear. [3 Mark]
Answer: Let A = (8, 7), B = (6, 4), C = (0, -5)

Out of the line segments AB, BC and AC, if the sum of two of them is equal to the third, then A, B, C are collinear.
The three given points A, B, C are collinear.
Question 4
Question: A point is equidistant from A (-6, 4) and B (2, -8). Find its co-ordinates, if its abscissa and ordinate are equal. [2 Mark]
Answer: 
Let P be the point which is equidistant from A and B. Since the abscissa and ordinates are equal, let (x, x) be the co-ordinates of P.
PA = PB (given)

Question 5
Question: The distance between A (1, 3) and B (x, 7) is 5. Calculate the possible values of x. [2 Mark]
Answer: ![]()
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Squaring both sides, we get
25 = x2- 2x + 17

Question 6
Question: What points on the x-axis are at a distance of 5 units from the point (5, -4)? [2 Mark]
Answer: Note that all the points on x-axis have y-co-ordinate zero. Let (x, 0) be the point which is at a distance of 5 units from the point (5, -4).
Using distance formula, we have
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Squaring both sides, we get
(5 - x)2+ 16 = 25

The points are (8, 0) and (2, 0).
Question 7
Question: What point on y-axis is equidistant from the points (7, 6) and (-3, 4)? [2 Mark]
Answer: Note that all the points on y-axis has x co-ordinate 0. Let P (0, y) be the point on Y axis which is equidistant from A (7,6) and B (-3,4).
PA = PB (given)
(7 - 0)2 + (6 - y)2
(- 3 - 0)2 + (4 - y)2
Squaring both sides and simplifying, we get
49 + 36 + y2- 12y = 9 + 16 - 8y + y2
-12y + 8y = 25 - 49 - 36
-4y = -60
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The point (0, 15) is equidistant from the points (7,6) and (-3,4).
Question 8
Question: A is a point on the y-axis whose ordinate is 5 and B is the point (-3, 1). Calculate the length of AB. [2 Mark]
Answer: The co-ordinates of A are (0,5)
B = (-3,-1) (given)
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Question 9
Question: Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11. [2 Mark]
Answer: The co-ordinates of B are (11, 0).
(on the x-axis, y = 0, abscissa = x-coordinate = 11)

Question 10
Question: A point A is at a distance
from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice of its abscissa. [3 Mark]
Answer: Ordinate is y-co-ordinate and Abscissa is x co-ordinate.
Let the co-ordinates of A be (x, y).
Then, y = 2x (given)
A is a point which has co-ordinates (x, 2x) and B (4, 3).


The two possible points are (3, 6) and (1, 2) .
