10th grade Perimeter and area of shapes on the coordinate plane worksheet

Perimeter and area of shapes on the coordinate plane

Grade 10 Math Worksheet

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

1. 1.

   Luz's tile has corners A(2, -4), B(5, 0), C(-3, 6), D(-6, 2). Which is the most specific shape the slopes and lengths prove it to be?

   • Parallelogram: both pairs of opposite sides are parallel and equal in length
   • Square: all four angles are right angles and all four sides are equal
   • Rectangle: opposite sides are parallel and AB ⊥ BC (slopes 4/3 and -3/4), so every angle is right, but AB ≠ BC
   • Rhombus: all four sides are equal, with AB = BC = 5, so the tile is a diamond with no right angles
2. 2.

   Milo's tile has corners A(-4, 0), B(0, 3), C(4, 0), D(0, -3). Which is the most specific shape the slopes and lengths prove it to be?

   • Rhombus: all four sides are 5, but AB and BC (slopes 3/4 and -3/4) are not perpendicular
   • Rectangle: opposite sides are parallel and AB ⊥ BC, with slopes 3/4 and -3/4, so the tile has right angles
   • Square: all four sides are equal and all four angles are right angles, since the corners look square
   • Parallelogram: both pairs of opposite sides are parallel and equal in length, and the coordinates prove nothing more
3. 3.

   Noah's tile has corners A(0, 0), B(3, 4), C(-1, 7), D(-4, 3). Which is the most specific shape the slopes and lengths prove it to be?

   • Rhombus only: all four sides are 5, but AB is not perpendicular to BC
   • Rectangle: opposite sides are parallel and AB ⊥ BC, so all angles are right angles
   • Square: all four sides are 5 and AB ⊥ BC (slopes 4/3 and -3/4)
   • Parallelogram only: opposite sides are parallel and equal, with no right angle
4. 4.

   Pia's tile has corners A(-4, -2), B(1, -1), C(4, 3), D(-1, 2). Which is the most specific shape the slopes and lengths prove it to be?

   • Trapezoid: AB ∥ DC (slope 1/5), but AD is not parallel to BC, so one pair of sides is parallel
   • Rectangle: opposite sides are parallel and equal in length, so the tile has right angles at the corners
   • Quadrilateral: the four corners are joined by four straight sides, and nothing more is proved by the coordinates
   • Parallelogram only: opposite sides are parallel and equal, but AB ≠ AD and AB is not perpendicular to AD
5. 5.

   Ren wants to prove ABCD is a parallelogram. Which computed fact is enough on its own?

   • The midpoint of AC is (0, 0.5), which lies inside the tile
   • AB = DC = √26, so the opposite sides are the same length
   • AB ∥ DC, both with slope 1/5
   • AB ∥ DC and AB = DC: both run 5 across and 1 up
6. 6.

   Tala has shown ABCD is a parallelogram and now wants to prove it is a rectangle. Which computed fact is enough?

   • The diagonals AC and BD bisect each other
   • AB = DC = 5
   • AB ∥ DC, both with slope 4/3
   • AC = BD: both diagonals have length √125
7. 7.

   Bo's bike path runs from A(-6, 2) to B(4, -8). Point P is on AB with AP:PB = 2:3. Where is P? Write it like (7, -3).
8. 8.

   Esme's kite path runs from A(-8, -4) to B(8, 4). Point P is on AB with AP:PB = 1:3. Where is P? Write it like (7, -3).
9. 9.

   Jun's map path runs from A(-5, -2) to B(7, 6). Point P is on AB with AP:PB = 3:1. Where is P? Write it like (7, -3).
10. 10.

    Kira's paper path runs from A(-7, 5) to B(5, -7). Point P is on AB with AP:PB = 1:2. Where is P? Write it like (7, -3).