Respuesta :
Solution:
Let us the line with the equation:
[tex]f(x)=y=\text{ 3-}\frac{1}{7}x[/tex]According to this equation, the slope of this line is:
[tex]m\text{ =-}\frac{1}{7}[/tex]now, the slope of the line perpendicular to the line f(x) would be:
[tex]m_p=7\text{ }[/tex]Since the perpendicular line to f(x), passes through the origin, we have that the y-intercept of this line is 0, so the equation of the perpendicular line passing through origin is:
[tex]y\text{ = 7x}[/tex]now, to find the intersecting point between the lines, we must equalize both equations of the lines:
[tex]7x\text{ = 3-}\frac{1}{7}x[/tex]then, solve for x:
[tex]x\text{ = }\frac{21}{50}[/tex]the y-coordinate corresponding to this x, is:
[tex]y\text{ = 7(}\frac{21}{50}\text{)=}\frac{147}{50}[/tex]thus, we obtain the point:
[tex](x,y)=(\frac{21}{50},\frac{147}{50})[/tex]now, the y-intercept of the given line f(x) is when x=0, then:
[tex]f(0)=y=\text{ 3-}\frac{1}{7}(0)=3[/tex]thus, we get the point:
[tex](x,y)=(0,3)[/tex]Therefore, we already have the 3 points that define the triangle
so the triangle is bounded by the points
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