Question

Pam walks along a road which can be modeled by the equation y=3x, where (0,0) represents her starting point. When she reaches the point (7,21), she turns right, so that she is traveling perpendicular to the original road, until she stops at a point which is due east of her starting point (in other words, on the x-axis).

What is the point where Pam stops?

Answer 1

(70,0)

Explanation:

Because Pam starts traveling perpendicularly to the road she started on when she gets to the point (7,21), we can use what we know about perpendicular lines to determine the equation of the line she is now on.

Remember that if a line has slope m, then a perpendicular line has slope −1m. So in this case, the slope is −13. Now we can use the point-slope form of the line, using the point (7,21) and the slope−13:

y−y0y−21=m(x−x0)=−13(x−7)

Finally, since we want to find the point where this line intersects the x-axis (where y=0), we can set y=0:

(0)−21=−13(x−7)

Now, multiplying through by −3 to clear the denominator, and solving for x, we find

(−3)(−21)6370=x−7=x−7=x

So the point where Pam reaches the x-axis is (70,0).

Answer 2

Pam stops at the point (14, 0), which is due east of her starting point (0, 0). This point can be calculated by taking the x-coordinate of her original position (7) and doubling it to get the new x-coordinate (14). Since she is now traveling on the x-axis, the y-coordinate is 0.