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.

   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?

   (-1, 1)
3. 2.

   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)
5. 3.

   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)
6. 4.

   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 3.

   (3, 1)
7. 5.

   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 3.

   (1, 1)
8. 6.

   Luz wants to balance a triangle cut from card on one fingertip. Its corners are D(-6, -2), F(0, 4) and G(3, -5). Where is the balance point (the centroid)?

   Use the picture in question 3.

   (-1, -1)
10. 7.

    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?

    • Yes: all three pairs of sides are equal (SSS).
    • No: they are in different places on the grid.
    • No: the triangles face different ways.
11. 8.

    Noah plots a shape on a grid map: triangle DFG with D(1, 1), F(4, 2), G(2, 4), and triangle QSU with Q(9, 1), S(6, 2), U(8, 4). Are they congruent?

    Use the picture in question 7.

    • No: the triangles face different ways.
    • No: they are in different places on the grid.
    • 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 7.

    • Yes: both triangles have a side of 4 or 5.
    • No: the third sides are √17 and 3.
    • Yes: two pairs of sides are equal.
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 7.

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