This creates a triangle with legs of 1.5 and 1.5; the hypotenuse (the distance from the origin) would then
be , or about 2.12. Do the same with (B), (C), and (D). The distance of (B) would be , or
about 1.4. Choices (C) and (D) lie in a straight line left and up from the origin, respectively, so the
distance of (C) is 0.5, and the distance of (D) is 1. The distance farthest from the origin is about 2.12,
which is (A).
Roots, Solutions, and x-intercepts
We’ve talked about y-intercepts in the discussion of the slope-intercept form of a line, and we talked
about solutions when we covered systems of equations. But what about x-intercepts, or the solution for
just one equation? A solution, sometimes called a root, is simply any point where a line or curve
intersects the x-axis. Similarly, just as the y-intercept was the point where a line crossed the y-axis, an “x-
intercept” is a point where a line or curve intersects the x-axis.
Keep these terms straight and you’ll be in great shape!
Let’s try a question that requires knowledge of intercepts and distance in the xy-plane.
15.What is the distance between the x-intercept and the y-intercept of the line y = x − 6?