Use coordinates to check a triangle or a quadrilateral

Grade 10 Math Worksheet

Circle the best answer.

1. 1.

   Tala plans a rug pattern on a grid: D(0, 0), F(3, 4), G(8, 4) and H(5, 0). Opposite sides are parallel. Which name fits it best?

   • rhombus
   • parallelogram
   • rectangle
   • square
2. 2.

   Zee designs a window pane on a grid: D(1, 1), F(3, 5), G(5, 1) and H(3, -3). Opposite sides are parallel. Which name fits it best?

   • parallelogram
   • square
   • rectangle
   • rhombus
3. 3.

   Ari plans a tabletop on a grid: D(0, 2), F(4, 0), G(7, 6) and H(3, 8). Opposite sides are parallel. Which name fits it best?

   • rhombus
   • square
   • parallelogram
   • rectangle
4. 4.

   Esme draws a shape on graph paper: D(1, 0), F(4, 2), G(2, 5) and H(-1, 3). Opposite sides are parallel. Which name fits it best?

   • rectangle
   • square
   • rhombus
   • parallelogram
5. 5.

   Jun plots a shape on a grid map: D(0, 0), F(5, 1), G(7, 4) and H(2, 3). Opposite sides are parallel. Which name fits it best?

   • square
   • parallelogram
   • rectangle
   • rhombus
7. 6.

   Kira plans a kite frame on a grid: D(4, 5), F(2, 1) and G(4, 0). Is the angle at F a right angle?

   • No: the sides FD and FG have different lengths.
   • Yes: the slopes 2 and -1/2 multiply to -1.
   • No: the two slopes are not equal.
8. 7.

   Milo plans a rug pattern on a grid: D(3, 5), F(1, 1) and G(3, -3). Is the angle at F a right angle?

   Use the picture in question 6.

   • Yes: the triangle looks like it has a square corner.
   • Yes: the slopes 2 and -2 are opposites.
   • No: the slopes 2 and -2 multiply to -4, not -1.
9. 8.

   Noah designs a window pane on a grid: D(-1, 6), F(-2, 3) and G(0, -3). Is the angle at F a right angle?

   Use the picture in question 6.

   • Yes: the slopes 3 and -3 are opposites.
   • Yes: the triangle looks like it has a square corner.
   • No: the slopes 3 and -3 multiply to -9, not -1.
10. 9.

    Pia plans a tabletop on a grid: D(3, 8), F(1, 2) and G(7, 4). Is the angle at F a right angle?

    Use the picture in question 6.

    • No: the slopes 3 and 1/3 multiply to 1, not -1.
    • Yes: the triangle looks like it has a square corner.
    • Yes: the slope 1/3 is 3 flipped.
11. 10.

    Ren draws the top of a box on a grid: D(2, 3), F(0, -1) and G(4, 1). Is the angle at F a right angle?

    Use the picture in question 6.

    • Yes: the triangle looks like it has a square corner.
    • No: the slopes 2 and 1/2 multiply to 1, not -1.
    • Yes: the slope 1/2 is 2 flipped.