Coordinates & Midpoint
A point is at (3, 5). Which quadrant is it in?
Quadrant I
(Easy) What angle do perpendicular lines form?
90°
(5, 7)
(Easy) What is the sum of interior angles of a triangle?
180°
(Easy) A right triangle has legs 3 cm and 4 cm. Find the hypotenuse.
5 cm
(Easy-Medium) What is the midpoint of A(2, 4) and B(6, 8)?
(4, 6)
(Easy-Medium) A transversal crosses two parallel lines. Co-interior angles add up to?
180°
(Easy-Medium) A point at (4, 5) is reflected across the x-axis. New coordinates
(4, –5)
(Easy-Medium) Two angles of a triangle are 60° and 80°. Find the third.
40°
(Easy-Medium) A right triangle has legs 5 cm and 12 cm. Find the hypotenuse.
13 cm
(Medium) Find the distance between (0, 0) and (6, 8).
10 units
(Hard) Two alternate angles are (3x + 10)° and (5x – 20)°. Find x.
115°
(Medium) A point at (0, 6) is rotated 90° anticlockwise about the origin. New coordinates?
(–6, 0)
(Medium) The exterior angle of a triangle is 120°. One remote interior angle is 55°. Find the other.
65°
(Medium) The hypotenuse is 15 cm and one leg is 9 cm. Find the other leg.
√(225 – 81) = √144 = 12 cm
(Hard) M is the midpoint of AB. A = (3, 7), M = (6, 2). Find B.
B = (9, –3)
(Hard) Two alternate angles are (3x + 10)° and (5x – 20)°. Find
3x + 10 = 5x – 20 → 30 = 2x → x = 15
(Hard) A shape with vertices (2, 3), (4, 3), (4, 6) is enlarged by scale factor 2 from the origin. Find the new vertices.
(4, 6), (8, 6), (8, 12)
(Hard) A pentagon has angles 110°, 95°, 130°, 105°. Find the fifth angle.
540° – (110 + 95 + 130 + 105) = 540 – 440 = 100°
(Hard) A rectangle has length 16 cm and width 12 cm. Find the length of the diagonal.
√(256 + 144) = √400 = 20 cm
(Very Hard) Point A is at (2, 5) and midpoint M is at (–1, 3). Point B lies on the line y = x + 1. Verify if B satisfies this equation.
B = (–4, 1) — yes, –4 + 1 + 1 = –2 ≠ –4+1= –3, so B does NOT satisfy y = x + 1
(Very Hard) A transversal crosses two parallel lines. One corresponding angle is (4x + 15)° and the other is (7x – 30)°. Find both angles.
4x + 15 = 7x – 30 → 45 = 3x → x = 15 → both angles = 75°
(Very Hard) Triangle A(1, 2), B(3, 2), C(2, 5) is reflected across the line y = x. Find the new coordinates of all three vertices.
A(2, 1), B(2, 3), C(5, 2)
(Very Hard) Each interior angle of a regular polygon is 156°. How many sides does it have?
Exterior angle = 180 – 156 = 24° → 360 ÷ 24 = 15 sides
(Very Hard) A ladder 25 m long leans against a wall. The base is 7 m from the wall. How high up the wall does the ladder reach? If the base is moved 2 m further away, how much does the ladder slide down?
Height = √(625 – 49) = √576 = 24 m. New base = 9 m → new height = √(625 – 81) = √544 ≈ 23.32 m → slides down by 0.68 m