Regular polygons and the coordinate plane
Answers are for parents and teachers.
1
A regular pentagon and a square share a side. Find the angle outside the two shapes at a vertex of the shared side.
The pentagon angle is 108° and the square angle is 90°. 360° − 108° − 90° = 162°.
2
Name the quadrant of A, B, C and D.
A(−3, 2) is in II. B(4, −5) is in IV. C(0, 6) is on the y-axis, in no quadrant. D(−2, −2) is in III.
3
Find the projections of E(−5, −3) on both axes. Then F is (2, 1): find the length of the projection of EF on each axis.
On the x-axis (−5, 0), on the y-axis (0, −3). Lengths: |2 − (−5)| = 7 on the x-axis and |1 − (−3)| = 4 on the y-axis.
4
Find the midpoint of (−6, −3) and (2, 5).
((−6 + 2) ÷ 2, (−3 + 5) ÷ 2) = (−2, 1).
5
ABCD is a parallelogram with A(−1, −1), B(3, 0) and C(4, 3). Find D and check your answer.
The midpoint of AC is (1.5, 1). D = (2 × 1.5 − 3, 2 × 1 − 0) = (0, 2). Check: AB goes 4 right and 1 up, and DC goes 4 − 0 = 4 right and 3 − 2 = 1 up.