An intercept is where a line meets an axis, and one coordinate is zero at each crossing. Graph the line in Desmos and click both intercepts. The axes make a right triangle whose legs run from the intercepts to the origin. The distance between the intercepts is the hypotenuse, not the sum of the leg lengths.
Hints
- Hint 1
Every point on the -axis has . Graph the line and click its vertical-axis crossing. What coordinates does Desmos show for ?
- Hint 2
At the -intercept, the -coordinate is . Click the line’s horizontal-axis crossing and check the sign of its -coordinate. Is left or right of the origin?
- Hint 3
The axes meet at a right angle. The two intercepts and the origin form a right triangle, with one leg along each axis. Which side of that triangle is the distance from to ?
Step-by-step
Graph the intercepts, then use the right triangle
Step 1Find the y-axis crossing
Type in Desmos. Click the line, then click its vertical-axis crossing. Desmos shows , so . The first coordinate is because every point on the -axis has .
- Step 2
Find the x-axis crossing
On the same graph, click the horizontal-axis crossing. Desmos shows , so ; every point on the -axis has . Keep the minus sign: is left of the origin.
- Step 3
Identify the side the question asks for
The axes meet at a right angle, so , , and the origin form a right triangle. Its legs, the sides meeting at that angle, have lengths along the -axis and along the -axis. The distance is the hypotenuse, the side across from the right angle.
- Step 4
Use the right-triangle side lengths
The -- right triangle has a hypotenuse of . Here the legs and are and each scaled by , so the hypotenuse scales to . The distance between and is . Choice C.