الرياضيات (بالإنجليزية) الصف السادس الابتدائي، الأسبوع 24: Points in all four quadrants: the signs of the coordinates

The coordinate plane and reflections

الأسبوع 24 · الأرباع الأربعة والأزواج المرتبة والانعكاس · 3 دروس

Points in all four quadrants: the signs of the coordinates

Discover Mathematics P6: Term 2, Unit 11, Lessons 1–3

GoalFind the quadrant of a point from the signs of its coordinates, and recognise points on the axes.

New words

sign · whether a number is positive (+) or negative (−)on an axis · a point with x = 0 or y = 0 lies on an axisanticlockwise · the direction opposite to the hands of a clock

Explanation

The signs of x and y tell us the quadrant. Quadrant I (top right): x positive, y positive (+, +). Quadrant II (top left): x negative, y positive (−, +). Quadrant III (bottom left): both negative (−, −). Quadrant IV (bottom right): x positive, y negative (+, −). A point with y = 0 lies on the x-axis, for example (4, 0). A point with x = 0 lies on the y-axis, for example (0, −3). A point on an axis is in NO quadrant. To find a quadrant, look at the sign of x first (left or right), then the sign of y (down or up).

Quadrant	Sign of x	Sign of y	Example
I (top right)	+	+	(3, 2)
II (top left)	−	+	(−3, 2)
III (bottom left)	−	−	(−3, −2)
IV (bottom right)	+	−	(3, −2)

Worked examples

In which quadrant is (−5, 6)? x is negative (left) and y is positive (up), so the point is in Quadrant II.

In which quadrant is (7, −1)? x is positive and y is negative, so the point is in Quadrant IV. And (−2, −8) has two negative signs, so it is in Quadrant III.

The points E(4, 0) and F(0, −3) are on the axes. E has y = 0, so it is on the x-axis. F has x = 0, so it is on the y-axis. Neither is in a quadrant.

Class activity

Quadrant game. Write eight ordered pairs on cards (two for each quadrant, using small numbers). Shuffle them. Pick a card and say its quadrant before you plot it. Plot it to check.

Practice

In which quadrant is (−4, −7)?

In which quadrant is (8, 3)?

Where is the point (0, 5)?

A point is in Quadrant IV. Which signs do its x and y have?

Write one point in each quadrant, using numbers from 1 to 9.