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Mathematics

Points P(x, 2), A(-2, 3) and B(-5, 4) are collinear.

Statement 1: Slope of PA = Slope of PB = Slope of AB.

Statement 2: x = 1.

  1. Both the statement are true.

  2. Both the statement are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Straight Line Eq

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Answer

Given, P(x, 2), A(-2, 3) and B(-5, 4).

If three points are collinear, it means they lie on same line.

∴ Slope will be equal.

∴ Slope of PA = Slope of PB = Slope of AB

So, statement 1 is true.

Using formula,

Slope = y2−y1x2−x1\dfrac{y2 - y1}{x2 - x1}

Slope of AB = Slope of PA

⇒4−3(−5)−(−2)=3−2(−2)−x⇒4−3−5+2=3−2−2−x⇒1−3=1−2−x⇒−2−x=−3⇒x=3−2⇒x=1.\Rightarrow \dfrac{4 - 3}{(-5) - (-2)} = \dfrac{3 - 2}{(-2) - x}\\[1em] \Rightarrow \dfrac{4 - 3}{-5 + 2} = \dfrac{3 - 2}{-2 - x}\\[1em] \Rightarrow \dfrac{1}{-3} = \dfrac{1}{-2 - x}\\[1em] \Rightarrow -2 - x = -3\\[1em] \Rightarrow x = 3 - 2\\[1em] \Rightarrow x = 1.

So, statement 2 is true.

Hence, option 1 is the correct option.

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