The Coordinate Plane: Problems with Solutions

Solution:
Horizontal

Solution:
Vertical

Solution:
2

Solution:
The x coordinate, which is always on the x-axis.

Solution:
The y coordinate, which is always on the y-axis.

Solution:
The distance from the point to the y-axis.

Solution:
The distance from the point to the x-axis.

Solution:
If the points are on the y-axis, their first coordinate is 0. If the points are at a distance of 3 units from the x-axis, their second coordinate can be 3 or -3. There are two points which fulfill both conditions: B(0, 3) and B'(0, -3).

Solution:
If the points are on the x-axis, their second coordinate is 0. If the points are at a distance of 2 units from the y-axis, their first coordinate can be 2 or -2. There are two points which fulfill both conditions: A(2, 0) and A'(-2, 0).

Solution:
4

Solution:
(0, 0)

Solution:
Point A is found in quadrant I,
so both its coordinates are positive.

Solution:
Point B is found in quadrant IV,
so its x-coordinate is positive and
its y-coordinate is negative.

Solution:
Point C is found in quadrant II,
so its x-coordinate is negative and
its y-coordinate is positive.

Solution:
Point D is found in quadrant III,
so both its coordinates are negative.

Solution:
Since both its coordinates are negative, point A is in quadrant III.

Solution:
Since its first coordinate is negative and the second one is positive, point B is in quadrant II.

Solution:
The coordinates of point A are (2, 1), since it is found in quadrant I at a distance of 2 units of length from the y-axis and 1 unit from the x-axis.

Solution:
The coordinates of point B are (-2, 3), since it is found in quadrant II at a distance of 2 units of length from the y-axis and 3 units from the x-axis.

Solution:
The coordinates of point C are (3, -4), since it is found in quadrant III at a distance of 3 units of length from the y-axis and 4 units from the x-axis.

Solution:
The coordinates of point D are (-1, -1), since it is found in quadrant IV at a distance of 1 units of length from the Y-axis and 1 unit from the x-axis.

Solution:
Point A is right on the x-axis, so its y-coordinate is 0. A is at a distance of 3 units to the right of the y-axis, so its x-coordinate is 3. Thus, the coordinates of point A are (3, 0).

Solution:
Point B is right on the y-axis, so its x-coordinate is 0. B is at a distance of 2 units from the x-axis, so its y-coordinate is 2. Thus, the coordinates of point B are (0, -2).

Solution:
Answer: A

Solution:
Since points B and C have the same y-coordinate, the length of BC is equal to the difference of the distances from the two points to the y-axis. The coordinates of B are (3, 2) and those of C are (6, 2). B is at a distance of 3 units from the y-axis and C is at a distance of 6 units from the y-axis. Thus, the length of BC is 6 - 3 = 3 units.

Solution:
Since points B and C have the same x-coordinate, the length of BC is equal to the difference of the distances from the two points to the x-axis. The coordinates of B are (3, 2) and those of C are (3, 4). B is at a distance of 2 units from the x-axis and C is at a distance of 4 units from the x-axis. Thus, the length of BC is 4 - 2 = 2 units.

Solution:
Since point A's coordinates are (4, 3), the distance from A to the x-axis is 3 units. Since point B's coordinates are (4, -2), the distance from B to the x-axis is 2 units. The length of AB is 3 + 2 = 5 units.

Solution:
Since point A's coordinates are (-3, 1), the distance from A to the y-axis is 3 units. Since point B's coordinates are (6, 1), the distance from B to the y-axis is 6 units. The length of AB is 3 + 6 = 9 units.

Solution:
The perimeter of a rectangle is 2L + 2l (= 2AB + 2BC).
Since point A's coordinates are (2, 3), the distance from A to the y-axis is 2 units. Since point B's coordinates are (6, 3), the distance from B to the y-axis is 6 units. Thus, AB = 6 - 2 = 4 units.
Since point C's coordinates are (6, 1), the distance from C to the x-axis is 1 unit and the distance from B to the x-axis is 3. Thus, BC = 3 - 1 = 2 units.
P = $2 \cdot 4 + 2 \cdot 2 = 8 + 4 = 12$

Solution:
The symmetric of point A with respect to the x-axis is at the same distance from the x-axis as A. Thus, its second coordinate is -3, the first coordinate remaining the same. The coordinates of the point are (2, -3).

Solution:
The symmetric of point A with respect to the y-axis is at the same distance from the y-axis as A. Thus, its first coordinate is -2, the second coordinate remaining the same. The coordinates of the point are (-2, 3).

Solution:
If point A moved 2 units higher, its y-coordinate would be 3 + 2 = 5. The x-coordinate would remain the same. The new coordinates would be (2, 5).

Solution:
If point B moved 2 units higher, its y-coordinate would be -4 + 2 = -2. The x-coordinate would remain the same. The new coordinates would be (3, -2).

Solution:
If point A moved 1 unit lower, its y-coordinate would be 3 - 1 = 2. The x-coordinate would remain the same. The new coordinates would be (2, 2).

Solution:
If point B moved 2 units lower, its y-coordinate would be -4 - 2 = -6. The x-coordinate would remain the same. The new coordinates would be (3, -6).

Solution:
If point A moved 3 units to the left, its x-coordinate would be 2 - 3 = -1. The y-coordinate would remain the same. The new coordinates would be (-1, 3).

Solution:
If point B moved 2 units to the right, its x-coordinate would be 3 + 2 = 5. The y-coordinate would remain the same. The new coordinates would be (5, -4).