If three points A- B and C lie on a line and A- 3-4- B- 7-7 and AC-10- then the coordinates of the point C can be

Given : A≡ (3,4), B≡ (7,7), AC≡ 10 Let the coordinates of C be (x, y) ⇒ AB=√((7 3)^2+(7 4)^2)=5 There are two possible cases: Case : 1 ⇒(x+32,y+42)=(7,7) ⇒ ...

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Standard XIII

Mathematics

Section Formula

If three poin...

Question

If three points $A, B$ and $C$ lie on a line and $A \equiv (3, 4),$ $B \equiv (7, 7)$ and $A C = 10$ , then the coordinates of the point $C$ can be

(10, 11)

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(11, 10)

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(- 5, - 2)

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(5, 2)

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Solution

The correct option is C $(- 5, - 2)$
Let the coordinates of $C$ be $(x, y)$
Given : $A \equiv (3, 4), B \equiv (7, 7), A C \equiv 10$
$\Rightarrow A B = \sqrt{4^{2} + 3^{2}} = 5$

There are two possible scenarios.

Case : $1$

$(\frac{x + 3}{2}, \frac{y + 4}{2}) = (7, 7) ∴ x = 11, y = 10 \Rightarrow C = (11, 10)$

Case : $2$

$C A : A B = 10 : 5 = 2 : 1$
$\Rightarrow (\frac{x + 14}{3}, \frac{y + 14}{3}) = (3, 4) \Rightarrow x = - 5, y = - 2$
$∴ C = (- 5, - 2)$

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Section Formula

Standard XIII Mathematics

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If three points A,B and C lie on a line and A≡(3,4), B≡(7,7) and AC=10, then the coordinates of the point C can be

The correct option is C (−5,−2)Let the coordinates of C be (x,y) Given : A≡(3,4),B≡(7,7),AC≡10 ⇒AB=√42+32=5 There are two possible scenarios. Case : 1 (x+32,y+42)=(7,7)∴x=11,y=10⇒C=(11,10) Case : 2 CA:AB=10:5=2:1 ⇒(x+143,y+143)=(3,4)⇒x=−5,y=−2 ∴C=(−5,−2)

If three points $A, B$ and $C$ lie on a line and $A \equiv (3, 4),$ $B \equiv (7, 7)$ and $A C = 10$ , then the coordinates of the point $C$ can be