Question

the area of the triangle formed by the points 0(0,0) A,(3,0) and B(0,6)is in sq. unit​

Answer 1

Step-by-step explanation:

By drawing the graph we can clearly see that this is a right angle triangle.

Area of right triangle = 1/2 * b * h

AO length :-

$= \sqrt{ {(0 - 3)}^{2} + {(0 - 0)}^{2} } \\ = \sqrt{ {(3)}^{2} + {(0)}^{2} } \\ = \sqrt{9 } \: \: \: \: = \: \: 3$

OB length :-

$= \sqrt{ {(0 - 0)}^{2} + {(0 - 6)}^{2} } \\ = \sqrt{ {(0)}^{2} + {(6)}^{2} } \\ = \sqrt{36} \: \: \: \: \: = \: \: \: 6$

AB length :-

$= \sqrt{ {(0 - 3)}^{2} + {(6 - 0)}^{2} } \\ = \sqrt{ {(3)}^{2} + {(6)}^{2} } \\ = \sqrt{9 + 36 } \: \: \: \: \: \: = \sqrt{45}$

Area of the triangle

$= \frac{1}{2} \times h \times b \\ = \frac{1}{2} \times 3 \times 6 \\ = \frac{1}{2} \times 18 \\ = 9 {cm}^{2}$