The vertex of a right angle of a right angled triangle lies on the straight line 2 x+y-10=0 and the two other vertices, at point (2,-3) and (4,1) then the area of triangle in sq. units is

Question

The vertex of a right angle of a right angled triangle lies on the straight line 2 x+y-10=0 and the two other vertices, at point (2,-3) and (4,1) then the area of triangle in sq. units is (A) √10 (B) 3 (C) (33/5) (D) 11

Tardigrade Admin · Accepted Answer

M 1 M 2=-1 ; (9-2 a / a -4) × (13-2 a / a -2)=-1 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/c75d786299882d699cb563aeaa34397f-.png" /> 117-26 a-18 a+4 a2 =-(a2-6 a+8) 5 a2-50 a+125=0 ; a=5 so B is (5,0) So area =(1/2) AB × AC =(1/2) √2 × 3 √2=3

Q. The vertex of a right angle of a right angled triangle lies on the straight line $2 x + y - 10 = 0$ and the two other vertices, at point $(2, - 3)$ and $(4, 1)$ then the area of triangle in sq. units is

$10$

$3$

$\frac{33}{5}$

$11$

$M_{1} M_{2} = - 1;$
$\frac{9 - 2 a}{a - 4} \times \frac{13 - 2 a}{a - 2} = - 1$

$117 - 26 a - 18 a + 4 a^{2}$
$= - (a^{2} - 6 a + 8)$
$5 a^{2} - 50 a + 125 = 0;$
$a = 5$ so $B$ is $(5, 0)$
So area $= \frac{1}{2} A B \times A C$
$= \frac{1}{2} 2 \times 32 = 3$

Q. The vertex of a right angle of a right angled triangle lies on the straight line 2x+y−10=0 and the two other vertices, at point (2,−3) and (4,1) then the area of triangle in sq. units is

10​

3

533​

11

M1​M2​=−1; a−49−2a​×a−213−2a​=−1 117−26a−18a+4a2 =−(a2−6a+8) 5a2−50a+125=0; a=5 so B is (5,0) So area =21​AB×AC =21​2​×32​=3

Q. The vertex of a right angle of a right angled triangle lies on the straight line $2 x + y - 10 = 0$ and the two other vertices, at point $(2, - 3)$ and $(4, 1)$ then the area of triangle in sq. units is

$10$

$3$

$\frac{33}{5}$

$11$

$M_{1} M_{2} = - 1;$
$\frac{9 - 2 a}{a - 4} \times \frac{13 - 2 a}{a - 2} = - 1$

$117 - 26 a - 18 a + 4 a^{2}$
$= - (a^{2} - 6 a + 8)$
$5 a^{2} - 50 a + 125 = 0;$
$a = 5$ so $B$ is $(5, 0)$
So area $= \frac{1}{2} A B \times A C$
$= \frac{1}{2} 2 \times 32 = 3$