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Standard XII

Mathematics

Section Formula

If A 1,1 and ...

Question

If $A (1, 1)$ and $B (2, - 3)$ are two points and $P (h, k)$ lies on the line $A B$ such that $P A = 3 A B$ , where $B$ lies in between $A$ and $P$ , then the value of $h - k$ is

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Solution

Given : $A P = 3 A B$
Let $A B = x$ , we get
$A P = 3 x \Rightarrow B P = 3 x - x = 2 x \Rightarrow \frac{A P}{B P} = \frac{3}{2}$

Hence, $P$ divides $A B$ externally in the ratio $3 : 2.$
$∴ P \equiv (\frac{3 \times 2 - 2 \times 1}{3 - 2}, \frac{3 \times (- 3) - 2 \times 1}{3 - 2})$
$\Rightarrow P \equiv (4, - 11) \Rightarrow h = 4, k = - 11 ∴ h - k = 15$

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Section Formula

Standard XII Mathematics

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If A(1,1) and B(2,−3) are two points and P(h,k) lies on the line AB such that PA=3AB, where B lies in between A and P, then the value of h−k is

Given : AP=3AB Let AB=x, we get AP=3x⇒BP=3x−x=2x⇒APBP=32 Hence, P divides AB externally in the ratio 3:2. ∴P≡(3×2−2×13−2,3×(−3)−2×13−2) ⇒P≡(4,−11)⇒h=4,k=−11∴h−k=15

If $A (1, 1)$ and $B (2, - 3)$ are two points and $P (h, k)$ lies on the line $A B$ such that $P A = 3 A B$ , where $B$ lies in between $A$ and $P$ , then the value of $h - k$ is