Mathematics
Find the equation of the line passing through the points P(5, 1) and Q(1, -1). Hence, show that the points P, Q and R(11, 4) are collinear.
Straight Line Eq
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Answer
The two given points are P(5, 1), Q(1, -1).
Slope of the line =
So, the equation of PQ is
⇒ y - y1 = m(x - x1)
⇒ y - 1 =
⇒ 2(y - 1) = x - 5
⇒ 2y - 2 = x - 5
⇒ x - 2y - 5 + 2 = 0
⇒ x - 2y - 3 = 0.
Now if point R(11, 4) is collinear to points P and Q then it will satisfy the equation x - 2y - 3 = 0,
Putting values in L.H.S of the equation
The equation of the line PQ is x - 2y - 3 = 0. Since, L.H.S. = 0 = R.H.S, thus R satisfies the equation. Hence, points P, Q and R are collinear.
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