The Use of Coordinates — The Cartesian System — Practice

Question 1

In which quadrant does (−5, 3) lie?

Accepted Answer

x is negative, y is positive → Quadrant II.

✦ Answer: Quadrant II.

Question 2

Where does the point (0, 7) lie?

Accepted Answer

x = 0, so it lies on the y-axis (7 units above the origin).

✦ Answer: on the y-axis.

Question 3

What is the abscissa of the point (−4, 9)?

Accepted Answer

The abscissa is the x-coordinate.

✦ Answer: −4.

Question 4

Are the points (2, 3) and (3, 2) the same? Justify.

Accepted Answer

Step 1 — Coordinates are an ordered pair (x, y).

Step 2 — (2, 3) has x = 2, y = 3; (3, 2) has x = 3, y = 2 — different positions.

✦ Answer: No; (x, y) ≠ (y, x) when x ≠ y.

Question 5

Classify A(−3, −7) and B(6, 0) by quadrant or axis.

Accepted Answer

A(−3, −7): both negative → Quadrant III.

B(6, 0): y = 0 → on the x-axis.

✦ Answer: A — Quadrant III; B — x-axis.

Question 6

State the coordinates of a point 5 units to the left of the origin and 2 units up.

Accepted Answer

Step 1 — left → x = −5; up → y = +2.

Step 2 — point is (−5, 2).

✦ Answer: (−5, 2) (Quadrant II).

Question 7

A point lies on the x-axis at distance 4 from the origin on the negative side. Another lies on the y-axis 3 units below the origin. Write both coordinates and name where each lies.

Accepted Answer

Step 1 — On the x-axis, y = 0; negative side at distance 4 → (−4, 0).

Step 2 — On the y-axis, x = 0; 3 units below → (0, −3).

✦ Answer: (−4, 0) on the x-axis; (0, −3) on the y-axis.

Question 8

Plot P(2, 3), Q(2, −3) and R(−2, 3). What kind of figure do P, Q, R and S(−2, −3) form?

Accepted Answer

Step 1 — P(2,3) and Q(2,−3) share x = 2; R(−2,3) and S(−2,−3) share x = −2.

Step 2 — Horizontal sides length 4, vertical sides length 6, all angles 90°.

✦ Answer: a rectangle (4 × 6).

Practice — The Use of Coordinates — The Cartesian System

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