The line $$x3+y4=1meets$$ the y and $$x-axis$$ at A and B, respectively. A square ABCD is constructed on the line segment AB away from the origin. The coordinates of the vertex of the square farthest from the origin are

Question

The line $$x3+y4=1meets$$ the y and $$x-axis$$ at A and B, respectively. A square ABCD is constructed on the line segment AB away from the origin. The coordinates of the vertex of the square farthest from the origin are

Infinity Learn · Accepted Answer

The coordinates of A are (0$$, $$4) and those of B are (3$$, $$0). $$BC=AB=32+42=5In$$ △BCL  ∠$$CBL=180-90-$$θ$$=90-$$θ$$sin$$(90-$$θ$$)=CLBCcos$$ θ$$=$$ CLBC and $$CL=BCcos$$⁡θ$$cos$$$$(90-$$θ$$)=BLBCor$$  $$BL=BCsin$$⁡θ or  $$BL=5$$×$$45=4$$ and $$CL=5$$×$$35=3$$ Similarly, $$MD=4$$ and $$AM=3$$ . So, the coordinates of C are $$(OB+BL$$,$$CL)≡(7$$,$$3) and those of D are (MD$$,$$OA+AM)≡$$4$$,$$7The$$ coordinates of the vertex farthest from the origin are (4$$,$$7).

The line $\frac{x}{3} + \frac{y}{4} = 1$ meets the y and x-axis at A and B, respectively. A square ABCD is constructed on the line segment AB away from the origin. The coordinates of the vertex of the square farthest from the origin are

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The line x3+y4=1meets the y and x-axis at A and B, respectively. A square ABCD is constructed on the line segment AB away from the origin. The coordinates of the vertex of the square farthest from the origin are

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The line $\frac{x}{3} + \frac{y}{4} = 1$ meets the y and x-axis at A and B, respectively. A square ABCD is constructed on the line segment AB away from the origin. The coordinates of the vertex of the square farthest from the origin are