Questions solved using Distance Formula

Question 21

Question:   Given A = (3, 1) and B = (0, y-1), find y if AB = 5. [2 Mark]

Answer:   

Question 22

Question:   Given A = (x+2, -2) and B = (11, 6). Find x if AB = 17. [2 Mark]

Answer:   

(9-x)² = 289 - 64 (9-x)² = 225



-x = 6 or -x = -24

Question 23

Question:   The centre of a circle is (2x-1, 3x+1). Find x if the circle passes through (-3, -1) and the length of the diameter is 20 units. [3 Mark]

Answer:    Radius = 10 units

The distance between the centre of the circle and any point on the circle = radius



(Squaring both sides)

Question 24

Question:   Find the distance between the following pairs of points. [Each 2 Mark]

(i) (2, 4), (6, 1)

(ii) (9, -13), (2, 11)

(iii) (7, -2), (-8, 6)

(iv) (5, 1), (5, -4)

Answer:    (i) Distance between two points A and B given by the formula, A(x₁, y₁), B(x₂, y₂)



Let A(x₁, y₁) = (2, 4),

B(x₂, y₂) = (6, 1)









= 5 units

(ii) Let A(9, -13), B(2, 11)













= 25 units.

(iii) (7, -2), (-8, 6)

Let A(7, -2), B(-8, 6)











= 17 units.

(iv) (5, 1), (5, -4)

Let A(5, 1), B(5, -4)









= 5 units

Question 25

Question:   Find the measures of the distance between the following: [Each 2 Mark]

(i) (a, 2a), (-2a, 6a)



(iii) (3.2, 8), (-1.6, 1.6)

Answer:    (i) Let A(a, 2a), B(-2a, 6a)











= 5a units

(ii)

Let













= 3 units

(iii) (3.2, 8), (-1.6, 1.6)

Let A(3.2, 8), B(-1.6, 1.6)











AB = 8 units





Distance between the points,



Substituting the values











= 12 units