Question

If area of triangle is 35 square units with vertices (2, −6), (5, 4), and ( k , 4). Then k is A. 12 B. −2 C. −12, −2 D. 12, −2

Answer 1

The given points are ( 2,−6 ),( 5,4 )and( k,4 ).

The area of triangle is 35 square units.

The formula used to determine the area of triangle is,

Δ= 1 2 | x 1 y 1 1 x 2 y 2 1 x 3 y 3 1 |

Here,

The area of triangle is 4 square units, the value of Δ can be positive or negative.

Δ=±35

x 1 =2 y 1 =−6

x 2 =5 y 2 =4

x 3 =k y 3 =4

Substitute the values in the above formula.

±35= 1 2 | 2 −6 1 5 4 1 k 4 1 |

Expand the determinant.

±35= 1 2 [ 2( 4−4 )−6( 5−k )+1( 20−4k ) ] ±70=[ 50−10k ] ±7=5−k

Solve for k.

The values are,

k=−2,12

Thus, option D is correct