If - - x 1 y 1 1- x 2 y 2 1- x 3 y 3 1 - - - - a 1 b 1 1- a 2 b 2 1- a 3 b 3 1 - then two triangles with vertices x 1 - y 1 - x 2 - y 2 - x 3 - y 3 and a 1 - b 1 - a 2 - b 2 - a 3 - b 3 are

The correct option is A equal in area [ | [ x_ 1 amp; y_ 1 amp; 1; x_ 2 amp; y_ 2 amp; 1; x_ 3 amp; y_ 3 amp ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Area of Triangle with Coordinates of Vertices Given

If | [ x 1...

Question

If $∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & 1 a_{2} & b_{2} & 1 a_{3} & b_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣$

then two triangles with vertices $(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})$ and $(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{3}, b_{3})$ are

equal in area

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

similar

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

congurent

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

with different areas

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

Open in App

Solution

Suggest Corrections

Similar questions

∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & 1 a_{2} & b_{2} & 1 a_{3} & b_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣

(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})

(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{3}, b_{3})

∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & 1 a_{2} & b_{2} & 1 a_{3} & b_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣

(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})

(a_{1}, b_{1})

(a_{2}, b_{2})

(a_{3}, b_{3})

∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 b_{1} & b_{2} & b_{3} a_{1} & a_{2} & a_{3} \end{matrix} ∣ ∣ ∣ ∣

(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})

(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{3}, b_{3})

∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 b_{1} & b_{2} & b_{3} a_{1} & a_{2} & a_{3} \end{matrix} ∣ ∣ ∣ ∣

(x_{1}, y_{1}), (x_{2}, y_{2}), ((x_{3}, y_{3})

(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{13}, b_{3}),

(x_{1}, y_{1}), (x_{2}, y_{2})

(x_{3}, y_{3})

⎡ ⎢ ⎣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ⎤ ⎥ ⎦

Join BYJU'S Learning Program