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

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

1. 1.

   P and the line y = 2; the shortest route from P meets the line at a right angle. Noah sits on a park bench at P(3, 7) on a grid. A straight path runs along y = 2. How far is P from it, in units?

   5
2. 2.

   P and the line y = -3; the shortest route from P meets the line at a right angle. Ren walks a dog from a gate at P(-4, 5) on a grid. A straight fence runs along y = -3. How far is P from it, in units?

   8
3. 3.

   P and the line x = 1; the shortest route from P meets the line at a right angle. Tala rides from a bike rack at P(6, -2) on a grid. A straight bike lane runs along x = 1. How far is P from it, in units?

   5
4. 4.

   Zee walks from a front door at P(-5, 4) on a grid. A straight sidewalk runs along x = 3. How far is P from it, in units?

   8
5. 5.

   P and the line y = 2; the shortest route from P meets the line at a right angle. Ari jogs from a water stop at P(8, -7) on a grid. A straight track runs along y = 2. How far is P from it, in units?

   9
6. 6.

   Bo marks a lookout on a trail map at P(7, 1) on a grid. A straight trail runs along x = -4. How far is P from it, in units?

   11
8. 7.

   Esme draws a straight road with slope 2 on a town map. What is the slope of a road perpendicular to it?

   -1/2
9. 8.

   Luz draws a straight road with slope -2/5 on a town map. What is the slope of a road perpendicular to it?

   Use the picture in question 7.

   5/2
10. 9.

    Milo draws a straight road with slope 4 on a town map. What is the slope of a road perpendicular to it?

    Use the picture in question 7.

    -1/4
11. 10.

    Noah draws a straight road with slope 3/4 on a town map. What is the slope of a road perpendicular to it?

    Use the picture in question 7.

    -4/3