1.
The co-ordinates of the end points of a diameter AB of a circle are A(-6, 8) and B(-10, 6). Find the co-ordinates of its centre.
Answer: Option 'A'
The center O is the mid point of AB.
Co-ordinates of O are [(-6-10)/2, (8+6)/2]
= -16/2, 14/2
= (-8, 7)
2.
Find the area of ΔABC whose vertices are A(2, -5), B(4, 9) and (6, -1).
Answer: Option 'D'
Here, x1 = 2, x2 = 4, x3 = 6 and y1 = -5, y2 = 9, y3 = -1
= 1/2 [2(9+1) + 4(-1+5) + 6(5-9)]
= 1/2 [2(10) + 4(4) + 6(-4)]
= 1/2 [20 + 16 - 24]
= 1/2 [12]
= 6 sq.units
3.
If the A(2, 3), B(5, k), and C(6, 7) are collinear, then k = ?
Answer: Option 'D'
x1 = 2, x2 = 5, x3 = 6 and y1 = 3, y2 = k, y3 = 7
Now Δ = 0 <=> 2(k - 7) + 5(7 - 3) + 6(3 - k) = 0
<=> 1/2 [2 (k-7) + 5(4) + 6(3-k)] = 0
<=> 2k - 14 + 20 + 18 - 6k = 0
<=> 24 - 4k = 0
<=> 4k = 24
<=> k = 6.
4.
If the points A(1, 2), B(2, 4), and C(k, 6) are collinear, then k = ?
Answer: Option 'B'
x1 = 1, x2 = 2, x3 = k and y1 = 2, y2 = 4, y3 = 6
= 1(4 - 6) + 2 (6 - 2) + k(2 - 4)
= -2 + 12 - 4 + 2k - 4k = 0
= 6 - 2k = 0
= -2k = 6
= k = -3.
5.
The distance between the points A(5, -7) and B(2, 3) is:
Answer: Option ''
AB2 = (2 - 5)2 + (3 + 7)2
=> (-3)2 + (10)2
=> 9 + 100 => √109