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9th grade · Math · Unit 19 of 19

Coordinate Geometry

Distance, midpoint and slope

What your child practices

Finding the distance between two points with the Pythagorean Theorem, the midpoint of a segment, slopes of segments, telling parallel and perpendicular lines apart, and using slopes to check for a right angle.

Oregon State Standards learning standard: HS.GM.D.14; HS.GM.A.3; HS.GM.D.13 · using the coordinate plane to find distances and midpoints, and using slopes to decide when lines are parallel or perpendicular

How we explain it

Children can open this short lesson before they practice.

  1. Distance: make a right triangle from the change in x and the change in y, then use the Pythagorean Theorem.
  2. Midpoint: average the x-coordinates and average the y-coordinates.
  3. Parallel lines have equal slopes. Perpendicular slopes multiply to −1.

Example: What is the distance from (1, 2) to (7, 10)? Change in x: 6. Change in y: 8. √(6² + 8²) = √100. Answer: 10

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    What is the distance between A(4, −6) and B(1, −10)?

    -10-10-9-9-8-8-7-7-6-6-5-5-4-4-3-3-2-2-1-1001122334455667788991010AB
    • 5
    • 7
    • 2
    • 1

  2. Question 2

    Triangle ABC has vertices A(1, 6), B(0, 2) and C(−8, 4). Is the angle at B a right angle?

    -10-10-9-9-8-8-7-7-6-6-5-5-4-4-3-3-2-2-1-1001122334455667788991010ABC
    • No
    • Yes

  3. Question 3

    What is the midpoint of the segment from (0, 3) to (−8, 7)?

    • (−4, 5)
    • (−8, 10)
    • (−4, 2)
    • (−3, 5)
    • (5, −4)

  4. Question 4

    Are the lines y = (5/3)x − 5 and y = (3/5)x − 6 parallel, perpendicular or neither?

    • Perpendicular
    • Neither
    • Parallel

  5. Question 5

    What is the slope of the segment from P(6, −5) to Q(0, −2)?

    • −1/2
    • 2
    • 1/2
    • −2

  6. Question 6

    A line has slope −2. What is the slope of a line perpendicular to it?

    • 2
    • 1/2
    • −2
    • −1/2

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