The point A divides the line segment joining the points (.-5,1.) and (.3,5.) in the ratio k:1 internally and the coordinates of points B and C are (1,5) and (7 , - 2) respectively. If the area of Δ ABC is 2 sq. units, then the sum of all the values of k is equal to

Question

The point A divides the line segment joining the points (.-5,1.) and (.3,5.) in the ratio k:1 internally and the coordinates of points B and C are (1,5) and (7 , - 2) respectively. If the area of Δ ABC is 2 sq. units, then the sum of all the values of k is equal to (A) (32/9) (B) 7 (C) (94/9) (D) (31/9)

Tardigrade Admin · Accepted Answer

A≡ ((3 k - 5/k + 1) , (5 k + 1/k + 1)) Area of Δ ABC=2 sq.units ⇒ (1/2)[(3 k - 5/k + 1) (5 + 2) + 1 (- 2 - (5 k + 1/k + 1)) + 7 ((5 k + 1/k + 1) - 5)]=±2 ⇒ 14k-66=±4(k + 1)⇒ k=7 or (31/9)

Q. The point $A$ divides the line segment joining the points $(- 5, 1)$ and $(3, 5)$ in the ratio $k : 1$ internally and the coordinates of points $B$ and $C$ are $(1, 5)$ and $(7, - 2)$ respectively. If the area of $Δ A BC$ is $2$ sq. units, then the sum of all the values of $k$ is equal to

$\frac{32}{9}$

$7$

$\frac{94}{9}$

$\frac{31}{9}$

Q. The point A divides the line segment joining the points (−5,1) and (3,5) in the ratio k:1 internally and the coordinates of points B and C are (1,5) and (7,−2) respectively. If the area of ΔABC is 2 sq. units, then the sum of all the values of k is equal to

932​

7

994​

931​

A≡(k+13k−5​,k+15k+1​) Area of ΔABC=2sq.units ⇒21​[k+13k−5​(5+2)+1(−2−k+15k+1​)+7(k+15k+1​−5)]=±2 ⇒14k−66=±4(k+1)⇒k=7 or 931​

Q. The point $A$ divides the line segment joining the points $(- 5, 1)$ and $(3, 5)$ in the ratio $k : 1$ internally and the coordinates of points $B$ and $C$ are $(1, 5)$ and $(7, - 2)$ respectively. If the area of $Δ A BC$ is $2$ sq. units, then the sum of all the values of $k$ is equal to

$\frac{32}{9}$

$7$

$\frac{94}{9}$

$\frac{31}{9}$