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ISEE Lower Level Mathematics Achievement Quiz

ISEE Lower Level Mathematics Achievement Quiz: Completing Grid Figures

Practice Completing Grid Figures in ISEE Lower Level Mathematics Achievement with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

Question 1 / 7

0 of 7 answered

A horizontal line segment starts at (3, 4) and ends at (9, 4). A vertical line segment starts at (3, 4) and ends at (3, 8). These are two sides of a rectangle. What is the fourth vertex of this rectangle?

Select an answer to continue

What this quiz covers

This quiz focuses on Completing Grid Figures, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Mathematics Achievement.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A horizontal line segment starts at (3, 4) and ends at (9, 4). A vertical line segment starts at (3, 4) and ends at (3, 8). These are two sides of a rectangle. What is the fourth vertex of this rectangle?

  1. (6, 6)
  2. (8, 9)
  3. (9, 4)
  4. (9, 8) (correct answer)

Explanation: The problem describes three vertices of the rectangle: the shared point (3, 4), the end of the horizontal segment (9, 4), and the end of the vertical segment (3, 8). The fourth vertex must align horizontally with (3, 8) (so its y-coordinate is 8) and vertically with (9, 4) (so its x-coordinate is 9). Therefore, the fourth vertex is (9, 8).

Question 2

The points A(2, 2) and B(5, 2) form the bottom side of a square. What are the coordinates of the vertex that is directly above point B?

  1. (2, 5)
  2. (5, -1)
  3. (5, 5) (correct answer)
  4. (8, 2)

Explanation: The side AB is horizontal and has a length of 5 - 2 = 3 units. Since it is the bottom side of a square, the other two vertices must be 3 units directly above points A and B. The vertex directly above B(5, 2) will have the same x-coordinate (5) and a y-coordinate that is 3 units greater (2 + 3 = 5). Thus, the coordinates are (5, 5).

Question 3

A student is drawing a rectangle on a coordinate grid. She has already plotted the points (8, 3), (2, 3), and (2, 7). Which point does she need to plot to complete the rectangle?

  1. (-4, 7)
  2. (7, 8)
  3. (8, -1)
  4. (8, 7) (correct answer)

Explanation: The points (2, 3) and (8, 3) form a horizontal side. The points (2, 3) and (2, 7) form a vertical side. Since these sides are perpendicular, they are adjacent sides of the rectangle. The fourth vertex must have the x-coordinate from the horizontal side's other point (8, 3) and the y-coordinate from the vertical side's other point (2, 7). Thus, the fourth vertex is (8, 7).

Question 4

Three corners of a square are located at (-1, -1), (3, -1), and (3, 3). What are the coordinates of the fourth corner?

  1. (-1, -5)
  2. (-1, 3) (correct answer)
  3. (1, -3)
  4. (7, 3)

Explanation: The side from (-1, -1) to (3, -1) is horizontal and has length 4. The side from (3, -1) to (3, 3) is vertical and has length 4. To complete the square, the fourth corner must have the x-coordinate of (-1, -1) and the y-coordinate of (3, 3). Therefore, the fourth vertex is at (-1, 3).

Question 5

Points (-3, 2), (4, 2), and (4, -1) are three vertices of a rectangle. What is the fourth vertex?

  1. (-3, -1) (correct answer)
  2. (-3, 5)
  3. (-1, -3)
  4. (11, -1)

Explanation: The side between (-3, 2) and (4, 2) is horizontal. The side between (4, 2) and (4, -1) is vertical. To complete the rectangle, the fourth vertex must align vertically with (-3, 2) (having an x-coordinate of -3) and horizontally with (4, -1) (having a y-coordinate of -1). Therefore, the fourth vertex is at (-3, -1).

Question 6

A rectangle has vertices at (1, 2), (7, 2), and (7, 5). What are the coordinates of the fourth vertex?

  1. (1, -1)
  2. (1, 5) (correct answer)
  3. (5, 1)
  4. (13, 5)

Explanation: The side from (1, 2) to (7, 2) is horizontal. The side from (7, 2) to (7, 5) is vertical. To form a rectangle, the fourth vertex must align horizontally with (7, 5) and vertically with (1, 2). This means it shares the x-coordinate of (1, 2) and the y-coordinate of (7, 5). The fourth vertex is (1, 5).

Question 7

Three vertices of a square are at the points (2, 1), (5, 1), and (5, 4). What are the coordinates of the fourth vertex?

  1. (2, -2)
  2. (2, 4) (correct answer)
  3. (4, 2)
  4. (8, 4)

Explanation: The vertices (2, 1) and (5, 1) form a horizontal side of length 3. The vertices (5, 1) and (5, 4) form a vertical side of length 3. To complete the square, the fourth vertex must have the x-coordinate of (2, 1) and the y-coordinate of (5, 4). Therefore, the fourth vertex is at (2, 4).