Medians, altitudes and bisectors: name them, and find where they meet

Answer Key - Grade 10 Math Worksheet

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

1. 1.

   Kira cuts a sandwich into triangle DFH with centroid G on median DQ. DG = (4x − 12) cm and GQ = (x + 9) cm. How long is DQ, in cm?

   72
2. 2.

   Luz draws ramp side DFH with centroid G on median DQ. DG = (5x − 5) inches and GQ = (x + 11) inches. How long is DQ, in inches?

   60
3. 3.

   Milo traces watermelon slice DFH with centroid G on median DQ. DG = (5x − 1) cm and GQ = (2x + 5) cm. How long is DQ, in cm?

   81
4. 4.

   Noah traces cheese wedge DFH with centroid G on median DQ. DG = (6x − 12) inches and GQ = (x + 8) inches. How long is DQ, in inches?

   45
6. 5.

   Ren marks three towns on a map, making triangle DFH with an obtuse angle at F. Where is the circumcenter of triangle DFH?

   • at the midpoint of the longest side, DH
   • outside the triangle
   • inside the triangle
   • at F, the vertex of the obtuse angle
7. 6.

   Zee draws the front of a wide tent as triangle DFH with an obtuse angle at F. Where is the incenter of triangle DFH?

   Use the picture in question 5.

   • inside the triangle
   • at F, the vertex of the obtuse angle
   • at the midpoint of the longest side, DH
   • outside the triangle
8. 7.

   Ari marks three towns on a grid map: D(1, 2), F(7, 4) and H(4, 9). What are the coordinates of the centroid of triangle DFH?

   (4, 5)
9. 8.

   Bo plans three park lamps on a grid: D(2, 1), F(8, 3) and H(5, 11). What are the coordinates of the centroid of triangle DFH?

   (5, 5)
10. 9.

    Esme plots three classrooms on a grid map of the school: D(0, 3), F(6, 0) and H(9, 9). What are the coordinates of the centroid of triangle DFH?

    (5, 4)
11. 10.

    Jun draws triangle DFH on grid paper: D(3, 6), F(10, 2) and H(5, 4). What are the coordinates of the centroid of triangle DFH?

    (6, 4)