What are the x- and y-coordinates of points on that lie on the y- and x-axis?
Graph:
Right triangle/Isosceles triangle?: Right Side lengths: DE=m, EF=n, DF=sqrt(m^2+n^2) Slope: m_(DE)=0, m_(EF)=Undefined, m_(DF)=- nm Midpoints: M_(DE)( m2,n), M_(EF)(m, n2), M_(DF)( m2, n2)
Practice makes perfect
Graphing the triangle
Any point that's on the x-axis has a y-coordinate of 0. Similarly, any point on the y-axis has an x-coordinate of 0. Therefore, it must be that
&F(m, 0) is on the $x-$axis
&D( 0,n) is on the $y-$axis.
Let's plot these points in a coordinate plane and draw DF.
The third point has the y-coordinate n and the x-coordinate m. This means FE has to be vertical and DE has to be horizontal. Since vertical and horizontal sides are perpendicular, we are dealing with a right triangle.
Finding length and slope
To find the slope of the sides, we can use the Slope Formula. Note that horizontal lines have a slope of 0 and vertical sides have an undefined slope. Therefore, the only side we need to determine the slope for by using the Slope Formula is DF.
To find the length of the sides, we can use the Distance Formula. However, we do not need to use the formula for the horizontal and vertical sides as their lengths are the absolute value of the difference between the endpoints' x-coordinates and y-coordinates, respectively.
DE:& |m-0|=m
EF:& |n-0|=n
The remaining side, we have to calculate with the Distance Formula.
