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9th grade · Math · Unit 2 of 16

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: A.2(E); A.2(F); A.3(A) · slopes of parallel and perpendicular lines and slope from two points

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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 2 of 16 in 9th grade Math, after Linear Relations and before Lines & Intersections.

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: Texas Education Agency (TEA)

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 = −(2/3)x + 1 and y = −(2/3)x − 2 parallel, perpendicular or neither?

    • Perpendicular
    • Neither
    • Parallel

  2. Question 2

    What is the slope of the segment from P(−5, 5) to Q(−7, 10)?

    • 5/2
    • −2/5
    • −3/2
    • −5/2

  3. Question 3

    Triangle ABC has vertices A(3, 3), B(4, 2) and C(2, 0). 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
    • Yes
    • No

  4. Question 4

    What is the distance between A(−2, 2) and B(−8, −6)?

    -10-10-9-9-8-8-7-7-6-6-5-5-4-4-3-3-2-2-1-1001122334455667788991010AB
    • 2
    • 14
    • 10
    • 12

  5. Question 5

    A line has slope 4. What is the slope of a line perpendicular to it?

    • −4
    • −1/4
    • 1/4
    • 4

  6. Question 6

    What is the midpoint of the segment from (4, 3) to (0, 7)?

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

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