Distance from a point to a line, and between two parallel lines

Answer Key - Grade 10 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Tala studies two straight rails on a grid: y = 2x + 1 and y = 2x + 11. Give an exact answer, simplified. How far apart are the rails?

   2√5
2. 2.

   Zee studies two straight rails on a grid: y = x − 2 and y = x + 4. Give an exact answer, simplified. How far apart are the rails?

   3√2
3. 3.

   Ari studies two straight rails on a grid: y = (1/2)x + 3 and y = (1/2)x + 8. Give an exact answer, simplified. How far apart are the rails?

   2√5

4. Read this first

   Grid

   The two parallel lines; a segment from S(1, -1) on the first meets the second at a right angle at F.

5. 4.

   Bo studies two straight rails on a grid: y = −3x + 2 and y = −3x + 22. Give an exact answer, simplified. How far apart are the rails?

   2√10
6. 5.

   P and the line y = −2x + 3. The shortest route meets the line at a right angle. Esme sits on a park bench at P(-3, -1), near a straight path along y = −2x + 3. Give an exact answer, simplified. What is the shortest distance from P to it?

   2√5
7. 6.

   Jun walks a dog from a gate at P(6, -7), near a straight fence along y = (1/3)x + 1. Give an exact answer, simplified. What is the shortest distance from P to it?

   3√10
8. 7.

   P and the line y = (3/2)x − 1. The shortest route meets the line at a right angle. Luz walks from a front door at P(-1, 4), near a straight sidewalk along y = (3/2)x − 1. Give an exact answer, simplified. What is the shortest distance from P to it?

   √13
9. 8.

   Milo jogs from a water stop at P(1, -3) and goes the shortest way to a straight track along y = −2x + 4. Where does the route meet it?

   (3, -2)

10. Grid

    P and the line y = 3x − 5; the route from P meets the line at a right angle at F.

11. 9.

    Noah marks a lookout on a trail map at P(5, 0) and goes the shortest way to a straight trail along y = 3x − 5. Where does the route meet it?

    (2, 1)

12. Grid

    P and the line y = −(1/3)x + 2; the route from P meets the line at a right angle at F.

13. 10.

    Ren sits on a park bench at P(6, 10) and goes the shortest way to a straight path along y = −(1/3)x + 2. Where does the route meet it?

    (3, 1)