The area of triangle formed by $(0, 0), (0, a)$ and $(b, 0)$ is .......... .

a b

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{a b}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

∣ ∣ ∣ \frac{a b}{2} ∣ ∣ ∣

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

| a b |

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $∣ ∣ ∣ \frac{a b}{2} ∣ ∣ ∣$
The area of a triangle formed by joining the points $(x_{1}, y_{1})$ , $(x_{2}, y_{2})$ and $(x_{3}, y_{3})$ is

$A = \frac{1}{2} ∣ ∣ ∣ y_{1} (x_{2} - x_{3}) + y_{2} (x_{3} - x_{1}) + y_{3} (x_{1} - x_{2}) ∣ ∣ ∣$

Therefore, the area of a triangle formed by joining the points $(0, 0)$ , $(0, a)$ and $(b, 0)$ is:

$A = \frac{1}{2} ∣ ∣ ∣ 0 (0 - b) + a (b - 0) + 0 (0 - 0) ∣ ∣ ∣$

$= \frac{1}{2} ∣ ∣ ∣ 0 + a b ∣ ∣ ∣$

$= ∣ ∣ ∣ \frac{a b}{2} ∣ ∣ ∣$

Hence, the area of the triangle is $∣ ∣ ∣ \frac{a b}{2} ∣ ∣ ∣$

Suggest Corrections

Similar questions

Q. Show that the area of the triangle formed by the lines

a x^{2} + 2 h x y + b y^{2} = 0

and

l x + m y + n = 0

\frac{n^{2} \sqrt{h^{2} - a b}}{∣ ∣ a m^{2} - 2 h l m + b l^{2} ∣ ∣}

Q. The line

a x + b y = a^{2} b^{2}

, will meet the y- axis at ____.

Q. Factorise

a^{3} - 27 b^{3} + 2 a^{2} b - 6 a b^{2}

Q. The length of the rectangle is

(4 a b + 6) m

and breadth of the rectangle is

(6 b^{2} + 2 a b) m

. Find the area of the rectangle.

Prove that the straight line $(a + b) x + (a - b) y = 2 a b, (a - b) x + (a + b) y = 2 a b$ and $x + y = 0$ form an isosceles triangle whose vertical angle is $2 t a n^{- 1} (\frac{a}{b})$ .

Join BYJU'S Learning Program

The area of triangle formed by (0,0),(0,a) and (b,0) is .......... .

The area of triangle formed by $(0, 0), (0, a)$ and $(b, 0)$ is .......... .