Geometry: Coordinate Geometry (Middle School) Worksheet

Question 1

Plot the point A(3, 5) on a coordinate plane. Describe how to move from the origin to reach point A.

Accepted Answer

To reach point A(3, 5), move 3 units to the right along the x-axis and then 5 units up. The point is in Quadrant I.

Question 2

Name the quadrant for each point: B(-4, 2), C(5, -3), D(-2, -6), and E(1, 4).

Accepted Answer

Point B is in Quadrant II, point C is in Quadrant IV, point D is in Quadrant III, and point E is in Quadrant I.

Question 3

A point is located 6 units left of the origin and 1 unit down. Write the ordered pair for the point and name its quadrant.

Accepted Answer

The ordered pair is (-6, -1). Since both coordinates are negative, the point is in Quadrant III.

Question 4

Points P(2, 3) and Q(2, -4) lie on a vertical line. Find the distance between the points.

Accepted Answer

The distance is 7 units. The x-coordinates are the same, so subtract the y-coordinates: 3 - (-4) = 7.

Question 5

Points R(-5, -2) and S(4, -2) lie on a horizontal line. Find the distance between the points.

Accepted Answer

The distance is 9 units. The y-coordinates are the same, so subtract the x-coordinates: 4 - (-5) = 9.

Question 6

Reflect the point M(4, -7) across the x-axis. Write the coordinates of the image point M'.

Accepted Answer

The image point is M'(4, 7). A reflection across the x-axis keeps the x-coordinate the same and changes the sign of the y-coordinate.

Question 7

Reflect the point N(-3, 6) across the y-axis. Write the coordinates of the image point N'.

Accepted Answer

The image point is N'(3, 6). A reflection across the y-axis changes the sign of the x-coordinate and keeps the y-coordinate the same.

Question 8

The vertices of a rectangle are A(-2, 1), B(4, 1), C(4, 5), and D(-2, 5). Find the length, width, and area of the rectangle.

Accepted Answer

The length is 6 units because 4 - (-2) = 6. The width is 4 units because 5 - 1 = 4. The area is 24 square units because 6 x 4 = 24.

Question 9

The vertices of a right triangle are J(0, 0), K(6, 0), and L(0, 4). Find the area of the triangle.

Accepted Answer

The area is 12 square units. The base is 6 units and the height is 4 units, so the area is 1/2 x 6 x 4 = 12.

Question 10

Find the missing coordinate for point T if T is on the x-axis and has an x-coordinate of -8.

Accepted Answer

The point is T(-8, 0). Every point on the x-axis has a y-coordinate of 0.

Question 11

Find the missing coordinate for point U if U is on the y-axis and has a y-coordinate of 9.

Accepted Answer

The point is U(0, 9). Every point on the y-axis has an x-coordinate of 0.

Question 12

A line segment has endpoints A(-1, 2) and B(5, 2). What is the midpoint of the segment?

Accepted Answer

The midpoint is (2, 2). The x-value halfway between -1 and 5 is 2, and the y-coordinate stays 2.

Question 13

A line segment has endpoints C(3, -4) and D(3, 8). What is the midpoint of the segment?

Accepted Answer

The midpoint is (3, 2). The x-coordinate stays 3, and the y-value halfway between -4 and 8 is 2.

Question 14

Plot the points A(-3, -2), B(2, -2), C(2, 3), and D(-3, 3). Connect the points in order and then connect D back to A. What shape is formed, and what is its perimeter?

Accepted Answer

The shape is a square. Each side is 5 units long, so the perimeter is 20 units.

Question 15

Point V is at (-2, 5). It is translated 4 units right and 6 units down. What are the coordinates of the new point V'?

Accepted Answer

The new point is V'(2, -1). Moving 4 units right changes the x-coordinate from -2 to 2, and moving 6 units down changes the y-coordinate from 5 to -1.

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Geometry: Coordinate Geometry (Middle School)

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