Question

La
Prove that the area of triangle whose vertices are (t,t-2),(t+2,t+and (t+3,t)is
independent of it.​

Answer 1

Step-by-step explanation:

Area = (1/2) |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |

So, here,

= (1/2) |t(t - t) + (t+2)(t - t+2) + (t+3)(t-2 - t) |

= (1/2) | t(0) + (t+2)(2) + (t+3)(-2) |

= (1/2) |0 + 2t + 4 - 2t - 6 |

= (1/2) | - 2 |

= 1/2 * 2

= 1, which is independent of t.

Hence area of this triangle is independent of t.