# Geometry - math word problems Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
2. Line segment Cut a line segment of 15 cm into two line segments so that their lengths are in ratio 2:1. What length will each have?
3. Ruler How far from Peter stands 2m hight John? Petr is looking to John over ruler that keeps at arm's distant 60 cm from the eye and on the ruler John measured the height of 15 mm.
4. Linear function What is the equation of linear function passing through points: a) A (0,3), B (3,0) b) A (-2,-6), B (3,4)
5. Forces Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
6. Dividing Divide the three line segment 13 cm, 26 cm and 19.5 cm long for parts so that the individual parts were equally long and longest. How long will the individual parts and how many it will?
7. Equilateral triangle ABC In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta
8. Resultant force Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25°
9. Forces on earth directions A force of 60 N [North] and 80 N [East] is exerted on an object wigth 10 kg. What is the acceleration of the object?
10. Rectangle 39 Find the perimeter and area of the rectangular with vertices (-1, 4), (0,4), (0, -1), and (-4, 4)
11. Points in plane The plane is given 12 points, 5 of which is located on a straight line. How many different lines could by draw from this points?
12. Slope Find the slope of the line: x=t and y=1+t.
13. Right triangle from axes A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
14. Hexagon cut pyramid Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.
15. Area of iso-trap Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other.
16. Cuboids Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633)
17. Points on line segment Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB.
18. Trapezoid - intersection of diagonals In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
19. Circle - AG Find the coordinates of circle and its diameter if its equation is: ?
20. Equation of circle find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.

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