CALCULATION: Given:
(p,p−3),(q+3,q) and
(6,3) are three points in a
2D plane.
Statement 1: The points lie on a straight line.
As we know that, if three points
A(x1,y1),B(x2,y2) and
C(x3,y3) aresaid to be collinear if the area of
∆ABC is zero i.e
||=0 Let
A=(p,p−3),B=(q+3,q) and
C=(6,3) ⇒|| =p(q−3)−(p−3)(q+3−6)+1(3q+9−6q) ⇒||=0 So, as we can see that area of triangle
ABC=0 for any value of
p and
q.
Hence, statement 1 is true.
Statement 2: The points alwayslie in the first quadrant only for any value of
p and
q. As we can see that, for any value of
p and
q it is not necessary that the points lies in the first quadrant only.
Hence, statement 2 is false.
Hence, the correct option is
1.