Geometry: Coordinate Geometry (Middle School)
Graphing points, finding distances, and working with shapes on the coordinate plane
Geometry: Coordinate Geometry (Middle School)
Graphing points, finding distances, and working with shapes on the coordinate plane
Geometry - Grade 6-8
- 1
Plot the point A(3, 5) on a coordinate plane. Describe how to move from the origin to reach point A.
The first number tells the horizontal movement, and the second number tells the vertical movement.
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. - 2
Name the quadrant for each point: B(-4, 2), C(5, -3), D(-2, -6), and E(1, 4).
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. - 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.
Left means a negative x-coordinate, and down means a negative y-coordinate.
The ordered pair is (-6, -1). Since both coordinates are negative, the point is in Quadrant III. - 4
Points P(2, 3) and Q(2, -4) lie on a vertical line. Find the distance between the points.
The distance is 7 units. The x-coordinates are the same, so subtract the y-coordinates: 3 - (-4) = 7. - 5
Points R(-5, -2) and S(4, -2) lie on a horizontal line. Find the distance between the points.
For a horizontal segment, compare only the x-coordinates.
The distance is 9 units. The y-coordinates are the same, so subtract the x-coordinates: 4 - (-5) = 9. - 6
Reflect the point M(4, -7) across the x-axis. Write the coordinates of the image point M'.
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. - 7
Reflect the point N(-3, 6) across the y-axis. Write the coordinates of the image point N'.
Across the y-axis, left and right switch places.
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. - 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.
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. - 9
The vertices of a right triangle are J(0, 0), K(6, 0), and L(0, 4). Find the area of the triangle.
Use the formula for the area of a triangle: area = 1/2 x base x height.
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. - 10
Find the missing coordinate for point T if T is on the x-axis and has an x-coordinate of -8.
The point is T(-8, 0). Every point on the x-axis has a y-coordinate of 0. - 11
Find the missing coordinate for point U if U is on the y-axis and has a y-coordinate of 9.
Points on the y-axis do not move left or right from the origin.
The point is U(0, 9). Every point on the y-axis has an x-coordinate of 0. - 12
A line segment has endpoints A(-1, 2) and B(5, 2). What is the midpoint of the segment?
The midpoint is (2, 2). The x-value halfway between -1 and 5 is 2, and the y-coordinate stays 2. - 13
A line segment has endpoints C(3, -4) and D(3, 8). What is the midpoint of the segment?
For a vertical segment, the midpoint has the same x-coordinate as the endpoints.
The midpoint is (3, 2). The x-coordinate stays 3, and the y-value halfway between -4 and 8 is 2. - 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?
The shape is a square. Each side is 5 units long, so the perimeter is 20 units. - 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'?
Right adds to x, and down subtracts from y.
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.