Coordinate Plane How Do You Know to Subtract

The Coordinate Airplane: Problems with Solutions

By Catalin David

Trouble 1

The x-axis is .

Problem 2

The y-axis is .

Problem 3

How many coordinates does any point in a plane have?

Trouble 4

The kickoff coordinate of the bespeak is called .

Solution:
The 10 coordinate, which is ever on the x-axis.

Trouble 5

The second coordinate of the point is .

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

Trouble vi

The x coordinate of a bespeak in a plane represents .

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

Problem seven

The y coordinate of a point in a plane represents .

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

Problem 8

How many points on the y-axis are at a distance of 3 units from the x-centrality?

Solution:
If the points are on the y-axis, their commencement coordinate is 0. If the points are at a distance of iii units from the 10-axis, their second coordinate can be 3 or -iii. There are two points which fulfill both weather: B(0, 3) and B'(0, -3).

Problem nine

How many points on the x-axis are at a distance of 2 units from the y-axis?

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 atmospheric condition: A(2, 0) and A'(-2, 0).

Problem x

How many quadrants are formed by the x- and y-axes in a plane?

Problem xi

The coordinates of the signal where the 10- and y-axes run into are .

Trouble 12

What are the signs of the 2 coordinates of point A?

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

Problem 13

What are the signs of the two coordinates of indicate B?

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

Trouble 14

What are the signs of the two coordinates of betoken C?

Solution:
Betoken C is establish in quadrant Ii,
so its 10-coordinate is negative and
its y-coordinate is positive.

Problem 15

What are the signs of the two coordinates of bespeak D?

Solution:
Betoken D is found in quadrant 3,
and so both its coordinates are negative.

Problem 16

Which quadrant contains signal A (-1, -i)?

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

Problem 17

Which quadrant contains betoken B (-2, 1)?

Solution:
Since its first coordinate is negative and the second one is positive, point B is in quadrant 2.

Problem 18

What are the coordinates of point A?

Solution:
The coordinates of bespeak A are (2, 1), since information technology is found in quadrant I at a altitude of two units of length from the y-axis and ane unit of measurement from the x-axis.

Problem 19

What are the coordinates of point B?

(ii, 3)

(3, -ii)

(-2, iii)

(-2, -3)

Solution:
The coordinates of point B are (-2, iii), 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.

Problem twenty

What are the coordinates of point C?

(-iv, iii)

(3, -4)

(-3, iv)

(-three, -four)

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

Trouble 21

What are the coordinates of indicate D?

(1, -one)

(ane, ane)

(-i, one)

(-i, -1)

Solution:
The coordinates of indicate D are (-1, -1), since it is found in quadrant 4 at a distance of i units of length from the Y-axis and i unit from the ten-axis.

Problem 22

What are the coordinates of signal A?

(0, 3)

(3, 3)

(-three, 0)

(three, 0)

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

Trouble 23

What are the coordinates of point B?

(-two, 0)

(0, -2)

(0, two)

(1, 1)

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

Problem 24

Which point has the coordinates (-3, 4)?

Problem 25

What is the length of BC?

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

Problem 26

What is the length of BC?

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 2 points to the x-axis. The coordinates of B are (3, two) and those of C are (3, four). B is at a distance of 2 units from the x-centrality and C is at a distance of four units from the ten-axis. Thus, the length of BC is 4 - 2 = 2 units.

Problem 27

What is the length of AB?

Solution:
Since point A's coordinates are (4, 3), the altitude from A to the 10-axis is iii units. Since signal B's coordinates are (4, -2), the distance from B to the ten-axis is 2 units. The length of AB is 3 + two = v units.

Problem 28

What is the length of AB?

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

Trouble 29

What is the perimeter of rectangle ABCD?

Solution:
The perimeter of a rectangle is 2L + 2l (= 2AB + 2BC).
Since signal A'due south coordinates are (2, iii), the altitude from A to the y-centrality is 2 units. Since point B's coordinates are (6, 3), the distance from B to the y-centrality is half dozen units. Thus, AB = 6 - 2 = iv units.
Since bespeak C's coordinates are (half-dozen, 1), the distance from C to the 10-axis is 1 unit and the distance from B to the ten-axis is 3. Thus, BC = iii - 1 = 2 units.
P = $2 \cdot 4 + ii \cdot ii = 8 + 4 = 12$

Trouble thirty

What are the coordinates of the symmetric of A with respect to the x-axis?

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

Problem 31

What are the coordinates of the symmetric of indicate A with respect to the y-axis?

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 signal are (-2, 3).

Problem 32

If bespeak A moved 2 units higher, what would its coordinates exist?

Solution:
If indicate A moved 2 units college, its y-coordinate would exist three + two = v. The x-coordinate would remain the same. The new coordinates would be (2, 5).

Trouble 33

If point B moved 2 units higher, what would its coordinates be?

(3, -6)

(five, -iv)

(3, -2)

(3, -4)

Solution:
If indicate B moved ii units higher, its y-coordinate would exist -iv + 2 = -2. The 10-coordinate would remain the aforementioned. The new coordinates would be (3, -2).

Problem 34

If point A moved 1 unit lower, what would its coordinates exist?

Solution:
If bespeak A moved 1 unit of measurement lower, its y-coordinate would exist three - i = two. The 10-coordinate would remain the same. The new coordinates would be (2, ii).

Problem 35

If indicate B moved 2 units lower, what would its coordinates be?

Solution:
If betoken B moved two units lower, its y-coordinate would exist -4 - two = -vi. The 10-coordinate would remain the same. The new coordinates would be (3, -6).

Trouble 36

If point A moved three units to the left, what would its coordinates exist?

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

Trouble 37

If point B moved two units to the right, what would its coordinates exist?

(3, -2)

(five, -4)

(5, -ii)

(one, -4)

Solution:
If bespeak B moved 2 units to the right, its x-coordinate would be three + two = five. The y-coordinate would remain the aforementioned. The new coordinates would be (5, -4).

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