To compare the side lengths of the triangle, we first need to graph the given vertices, A(5,0), B(0,8), and C(0,0). Then we can connect the vertices with straight lines.
Notice that BC lies on the y -axis and AC lies on the x -axis. We can look at each of the axes as line segments and use the Ruler Postulate to determine the coordinates of these points.
Ruler Postulate
Every point on a line can be paired with a real number. This makes a one-to-one correspondence between the points on the line and the real numbers. The real number that corresponds to a point is called the coordinate of the point.
The distance between two points is the absolute value of the difference of their coordinates. Looking at the axes we can see that the coordinate of the point B is 8, the coordinate of point C is 0, and the coordinate of A is 5.
Vertical Segment:& | 8- 0|=8 ⇒ BC=8
Horizontal Segment:& | 5- 0|=5 ⇒ AC=5
Next, we will find the length of hypotenuse by using the Distance Formula. The endpoints of AB are A( 5, 0) and B( 0, 8).
