Refer to IJKL
(a) The mid-point of the segment joining the points I(6,6) and J(6, 18) is
(i) (7,9)
(iii) (6, 12)
(iv) (12.24)
Refer to EFGH
(6) The distance between points H(10,6) and F(14, 18) is
(1) 8V5 unit (ii) 4/10 unit (iii) 18 unit
(iv) 24 unit
(i) (12.
has AB
15
NE
FILTU
LES
Refer to ABCD
(c) The coordinates of the points A and B are (22, 6) and (22; 18) respectively. The x-coordinate
of a point R on the line segment AB such that
AR 3
5.
(1) 18
(ii) 24
(ül) 22
(iv) 31
Refer to MQ
(d) The ratio in which the points (20, k) divides the line segment joining the points M(4,2)
and Q(24, 2) is
(ii) 16:15
(iii) 8:21
(iv) 10:17
Answers
(a) The mid-point of the segment joining the points I(6,6) and J(6, 18) is
(i) (7,9)
(iii) (6, 12)
(iv) (12.24)
Answer :-
Let mid - points is (x and y)
so,
→ x = (x1 + x2)/2 = (6 + 6)/2 = 12/2 = 6
→ y = (y1 + y2)/2 = (6 + 18)/2 = 24/2 = 12 .
therefore, mid points are (iii) (6, 12) .
(b) The distance between points H(10,6) and F(14, 18) is
(i) 8√5 unit
(ii) 4√10 unit
(iii) 18 unit
(iv) 24 unit
Answer :-
→ HF = √(x2 - x1)² + (y2 - y1)² = √(14 - 10)² + (18 - 6)² = √(4² + 12²) = √(16 + 144) = √(160 = 4√10 units (ii)
(d) The ratio in which the points (20, k) divides the line segment joining the points M(4,2) and Q(24, 2) is
(ii) 16:15
(iii) 8:21
(iv) 10:17
Answer :- Let (20,k) divides in ratio of m : n .
so,
→ 20 = (m*24 + n*4)/(m + n)
→ 20m + 20n = 24m + 4n
→ 20n - 4n = 24m - 20m
→ 16n = 4m
→ m /n = 16/4
→ m : n = 4 : 1 (Ans.)
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