# Geometry - math word problems

1. Find parameters Find parameters of the circle in the plane - coordinates of center and radius: ?
2. Lighthouse Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea
3. Trapezium diagonals It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC.
4. MG=7x-15, MG=7x-15, FG=33, x=? Point M is the midpoint of FG. Find unknown x.
5. Midpoint 6 FM=8a+1, FG=42, a=? Point M is the midpoint of FG. Find unknown a.
6. Find midpoint FM=5y+13, MG=5-3y, FG=? M is the midpoint of FG. Use the given information to find the missing measure or value.
7. Midpoint 5 FM=3x-4, MG=5x-26, FG=? Point M is the midpoint of FG. Use the given information to find the missing measure or value.
8. A screen A screen is 1680 x 1050 pixels. What are the coordinates (and size in pixels) of an centered area which is exactly 33% of the screen size?
9. Coordinates of square vertices The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square.
10. Diagonals at right angle In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD? Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
12. Scalar product Calculate the scalar product of two vectors: (2.5) (-1, -4)
13. Vertices of a right triangle Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
14. Circle described The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
15. Symmetry by plane Determine the coordinates of a image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0
16. Rectangular trapezoid The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the
17. Midpoint 4 If the midpoint of a segment is (6,3) and the other end point is (8,-4) what are thw coordinate of the other end?
18. Coordinates of midpoint If the midpoint of the segment is (6,3) and the other end is (8,4) what are the coordinate of the other end?
19. Three points Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
20. Center of line segment Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .

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