Section 4

Activities, Drills & Games

Practice is what turns a rule into a skill. Work through the five activities below: plot points by clicking, name quadrants against the clock, measure projections, compute midpoints, and finish with a scored quiz covering the whole lesson.

Guide

How to use this section

  • Activity 1 trains plotting: read the ordered pair, then click the exact spot.
  • Activity 2 trains the sign rule for quadrants and the special cases on the axes.
  • Activity 3 trains projections and the length |x₂ − x₁| and |y₂ − y₁|.
  • Activity 4 trains the midpoint formula, including fractional answers.
  • Activity 5 is a final quiz with explanations for every question.

Play & learn

Interactive Activities

Activity 1 — Click to Plot

Score 0 / 0

Click on the plane at the position of the point (2 , 2).

xy-6-6-4-4-2-2224466

Move right/left for x, up/down for y.

Activity 2 — Quadrant Sprint

Score 0 / 0

Where is the point (-2 , -1) located?

1st (+,+)2nd (−,+)3rd (−,−)4th (+,−)xy-6-6-4-4-2-2224466

Activity 3 — Projection Drill

For the segment AB with A(-1 , -4) and B(-3 , 3), give the length of its projection on each axis.

xy-6-6-4-4-2-2224466AB

Activity 4 — Midpoint Challenge

Find the midpoint M of the segment joining A(-4 , -2) and B(-3 , 3). Decimals such as 2.5 are allowed.

xy-6-6-4-4-2-2224466AB

Check your mastery

Assessment

Activity 5 — Final Quiz

Answer all eight questions, then submit to see your score and the explanations.

  1. 1. In which quadrant does the point (-7 , 3) lie?

  2. 2. The projection of the point (5 , -2) on the x-axis is:

  3. 3. The projection of the point (5 , -2) on the y-axis is:

  4. 4. The midpoint of the segment joining (2 , 6) and (8 , 2) is:

  5. 5. A point with coordinates (0 , -4) lies:

  6. 6. The length of the projection of AB on the x-axis, where A(-3 , 1) and B(4 , 5), is:

  7. 7. M(1 , 0) is the midpoint of AB and A(-2 , 3). Then B is:

  8. 8. Which statement is always true?

Homework

Extra Written Exercises

  1. 1. Plot A(4 , 0), B(0 , -5), C(-3 , -3) and name the position of each.
  2. 2. Find the projections of D(-6 , 2) on both axes.
  3. 3. AB has A(-2 , 7) and B(6 , -1). Find the length of each projection.
  4. 4. Find the midpoint of the segment joining (-9 , 4) and (3 , -10).
  5. 5. M(-1 , 2) is the midpoint of PQ with P(3 , 5). Find Q.
  6. 6. ABCD has A(-3 , 0), B(0 , 4), C(5 , 0), D(2 , -4). Show that the diagonals have the same midpoint.