Area of the triangle formed by (1, 1), (2, 5), (5, 2)

7.5

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

5.7

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

Open in App

Solution

The correct option is A 7.5
We know we can find the area of triangle formed by $(a_{1}, b_{1}), (a_{2}, b_{2}) a n d (a_{3}, b_{3})$ using the formula
$\frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & 1 a_{2} & b_{2} & 1 a_{3} & b_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣$
$∴ A r e a = \pm \frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 2 & 5 & 1 5 & 2 & 1 \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ \begin{matrix} \frac{1}{2} (1 (5 - 2) - 1 (2 - 5) + 1 (4 - 25)) \end{matrix} ∣ ∣$
$= ∣ ∣ \begin{matrix} \frac{1}{2} (3 + 3 - 21) \end{matrix} ∣ ∣ = \frac{15}{2} = 7.5 s q . m t s .$

Suggest Corrections

I. The centroid of the triangle formed by $(2, 3, - 1), (5, 6, 3), (2, - 3, 1)$ is	a) $(2, 2, 2)$
II. The circumcentre of the triangle formed by $(1, 2, 3), (2, 3, 1), (3, 1, 2)$ is	b) $(3, 1, 4)$
III. The orthocenter of the triangle formed by $(2, 1, 5), (3, 2, 3), (4, 0, 4)$ is	c) $(1, 1, 0)$
IV. The incentre of the triangle formed by $(0, 0, 0), (3, 0, 0), (0, 4, 0)$ is	d) $(3, 2, 1)$
	e) $(0, 0, 0)$