Coordinated Trouble #5

Geometry Level 3

Through the point ( 3 , 4 ) (3,4) are drawn two straight lines each inclined at 4 5 ∘ 45 ^ \circ to the straight line x − y = 2 x-y=2 . Find the area included by the three lines.


The answer is 4.5.

Soummo Mukherjee by Soummo Mukherjee , 25, India

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1 solution

Tom Engelsman
Dec 13, 2019

Pretty simple: draw the lines x = 3 , y = 4 x = 3, y = 4 to the line y = x − 2 y = x - 2 and you end up with a right isosceles triangle of side length 3. Thus, the area computes to 1 2 ⋅ 3 2 = 4.5 . \frac{1}{2} \cdot 3^{2} = \boxed{4.5}.

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