A right triangle is formed by the x-axis, the y-axis and the line #y = -2x + 3#. What is the length of the hypotenuse?

1 Answer
Jim G.
May 19, 2018

#3/2sqrt5~~3.35" to 2 dec. places"#

Explanation:

#"we require to find the intercepts, that is where the graph"#
#"crosses the x and y axes"#

#• " let x = 0, in the equation for y-intercept"#

#• " let y = 0, in the equation for x-intercept"#

#x=0rArry=0+3=3larrcolor(red)"y-intercept"#

#y=0rArr-2x+3=0rArrx=3/2larrcolor(red)"y-intercept"#

#"to find the hypotenuse (h) use "color(blue)"Pythagoras' theorem"#

#rArrh=sqrt(3^2+(3/2)^2)#

#color(white)(h)=sqrt(9+9/4)=sqrt(45/4)=(3sqrt5)/2~~3.35#

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