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9th grade · Math · Unit 5 of 18

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.

Alabama Course of Study content standard: GDA.18; GDA.32; GDA.33 · distance, midpoint and slope on the coordinate plane, and the slopes of parallel and perpendicular lines

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

Coordinate Geometry in Alabama

In the Alabama Course of Study, this is unit 5 of 18 in 9th grade Math, after Linear Relations and before Similarity & Scale.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Alabama State Department of Education (ALSDE)

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

    Are the lines y = (5/3)x + 4 and y = (3/5)x + 2 parallel, perpendicular or neither?

    • Perpendicular
    • Parallel
    • Neither

  2. Question 2

    What is the distance between A(−5, 5) and B(−1, 2)?

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

  3. Question 3

    What is the midpoint of the segment from (1, 6) to (5, −2)?

    • (6, 4)
    • (3, 2)
    • (2, −4)
    • (4, 2)
    • (2, 3)

  4. Question 4

    Triangle ABC has vertices A(2, −2), B(−1, 1) and C(2, 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

  5. Question 5

    What is the slope of the segment from P(0, 1) to Q(−5, 7)?

    • 6/5
    • −6/5
    • −1/5
    • −5/6

  6. Question 6

    A line has slope 2/3. What is the slope of a line perpendicular to it?

    • −3/2
    • −2/3
    • 3/2
    • 2/3

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