Question
Download Solution PDFConsider the following statements in respect of the points (p, p - 3), (q + 3, q) and (6, 3):
1. The points lie on a straight line.
2. The points always lie in the first quadrant only for any value of p and q.
Which of the above statements is/are correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
The three points A (x1, y1), B (x2, y2) and C (x3, y3) are said to be collinear if the area of Δ ABC is zero i.e
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) are said to be collinear if the area of Δ ABC is zero i.e
Let A = (p, p - 3), B = (q + 3, q) and C = (6, 3)
⇒
⇒
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 always lie 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.
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