Use coordinates to check a triangle or a quadrilateral

Answer Key - Grade 10 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

2. 1.

   Tala draws a shape on graph paper. DFGH is a parallelogram with D(1, 1), F(4, 2) and G(6, 5). Where is H?

   (3, 4)
3. 2.

   Zee plots a shape on a grid map. DFGH is a parallelogram with D(-2, 0), F(3, 1) and G(5, 4). Where is H?

   Use the picture in question 1.

   (0, 3)
4. 3.

   Ari plans a kite frame on a grid. DFGH is a parallelogram with D(0, -3), F(4, -1) and G(3, 3). Where is H?

   Use the picture in question 1.

   (-1, 1)
5. 4.

   Bo designs a quilt patch on a grid. DFGH is a parallelogram with D(-4, 2), F(-1, -2) and G(3, 1). Where is H?

   Use the picture in question 1.

   (0, 5)
7. 5.

   Esme wants to balance a triangle cut from card on one fingertip. Its corners are D(0, 0), F(6, 3) and G(3, 9). Where is the balance point (the centroid)?

   (3, 4)
8. 6.

   Jun wants to balance a triangle cut from card on one fingertip. Its corners are D(-2, 1), F(4, -3) and G(7, 5). Where is the balance point (the centroid)?

   Use the picture in question 5.

   (3, 1)
9. 7.

   Kira wants to balance a triangle cut from card on one fingertip. Its corners are D(1, -4), F(5, 2) and G(-3, 5). Where is the balance point (the centroid)?

   Use the picture in question 5.

   (1, 1)
11. 8.

    Milo draws a shape on graph paper: triangle DFG with D(0, 0), F(3, 0), G(0, 4), and triangle QSU with Q(5, 1), S(5, 4), U(9, 1). Are they congruent?

    • No: they are in different places on the grid.
    • No: the triangles face different ways.
    • Yes: all three pairs of sides are equal (SSS).
12. 9.

    Pia plans a kite frame on a grid: triangle DFG with D(0, 0), F(4, 0), G(3, 4), and triangle QSU with Q(6, 0), S(10, 0), U(10, 3). Are they congruent?

    Use the picture in question 8.

    • Yes: two pairs of sides are equal.
    • Yes: both triangles have a side of 4 or 5.
    • No: the third sides are √17 and 3.
13. 10.

    Ren designs a quilt patch on a grid: triangle DFG with D(0, 0), F(5, 0), G(0, 5), and triangle QSU with Q(6, 0), S(11, 0), U(9, 4). Are they congruent?

    Use the picture in question 8.

    • Yes: both triangles have a side of 4 or 5.
    • Yes: two pairs of sides are equal.
    • No: the third sides are √50 and √20.