1.
Find the value of k for which the points A(-2, 5), B(3, k) and C(6, 1) are collinear.
Answer: Option 'D'
x>1 = -2, x>2 = 3, x>3 = 6 and y>1 = 5, y>2 = k, y>3 = -1
Now Δ = 0 <=> -2(k + 1) + 3(-1 + 5) + 6(5 - k) = 0
<=> -2 (k+1) + 3(4) + 6(5-k) = 0
<=> -2k-2 + 12+30 -6k = 0
<=> 40 - 8k = 0
<=> -8k = -40
<=> k = 5.
2.
In which quadrant does the point(-4, -7) lie?
Answer: Option 'C'
The point (-4, -7) lies in 3rd quadrant.
3.
Find the distance of the point A(3, -3) from the origin.
Answer: Option 'A'
OA = √32+(-3)2 = √9+9 = √18 = 3√2
4.
If the distance of the point P(x, y) from A(a, 0) is a + x, then y2 = ?
Answer: Option 'C'
√(x-a)2+(y-0)2 = a + x
= (x-a)2+y2
= (a+x)2 => y2 = (x-a)2-(x-a)2-4ax => y2 = 4ax
5.
In which quadrant does the point(9, 0) lie?
Answer: Option 'A'
The point (9, 0) lies in y-axis.