الأسبوع 24 · قانون المساحة والمستوى الإحداثي · 3 دروس
3
Plotting points to make designs
Discover Mathematics P5: Term 2, Unit 10, Lessons 5–8
GoalPlot points from ordered pairs, join them to make a design, and find a missing corner.
New words
plot · to mark a point on a grid from its ordered pairvertex · a corner of a shapedesign · a picture made by joining plotted points in order
Explanation
To plot a point, start at the origin, go across by the first number, then go up by the second number, and mark the point. To make a design, plot all the points and join them in the order they are given, and then join the last point back to the first. The points (2, 1), (6, 1), (6, 4), (4, 6) and (2, 4) make the outline of a little house. We can use coordinates to find lengths: when two points have the same y-number, they lie on a horizontal line and the distance is the difference of the x-numbers. When they have the same x-number, they lie on a vertical line and the distance is the difference of the y-numbers. If you know three corners of a rectangle, the fourth corner takes the x-number of one corner and the y-number of another.
Worked examples
Plot (2, 1), (6, 1), (6, 4), (4, 6), (2, 4) and join them in order. The result is a pentagon that looks like a house with a pointed roof.
Three corners of a rectangle are (1, 2), (6, 2) and (6, 5). The fourth corner has x = 1 (same as the first corner) and y = 5 (same as the third corner): (1, 5). The width is 6 − 1 = 5 and the height is 5 − 2 = 3, so the area is 5 × 3 = 15 and the perimeter is 2 × (5 + 3) = 16.
A path goes from (0, 0) to (4, 0) and then to (4, 3). The first part is 4 units along the x-axis direction and the second part is 3 units up. The path is 4 + 3 = 7 units long.
Class activity
Secret picture. On squared paper make a 10 by 10 grid. Write 6 or more ordered pairs that make a simple picture (a boat, a tent, a star) and give them to a friend in order. Your friend plots and joins them. Does the picture match yours?
Practice
1
Plot (1, 1), (4, 1), (4, 3) and (1, 3) and join them. What shape is it and what is its area?
A rectangle 3 units by 2 units. Area 3 × 2 = 6 square units.
2
Three corners of a square are (2, 2), (5, 2) and (5, 5). Find the fourth corner and the area.
The fourth corner is (2, 5). The side is 5 − 2 = 3, so the area is 3 × 3 = 9 square units.
3
How far apart are (3, 1) and (3, 6)?
They have the same x-number, so the distance is 6 − 1 = 5 units.
4
Plot (1, 1), (5, 1) and (3, 4). The apex (3, 4) is above the middle of the base. What kind of triangle do you get, by its sides?
Isosceles: the two slanted sides are equal because the apex is in the middle.
5
Marwan walks from (1, 1) to (6, 1) and then to (6, 4). How many units does he walk?
