# Geometry - math word problems

1. On line
On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
2. Coordinates of vector
Determine the coordinate of a vector u=CD if C(19;-7) and D(-16;-5)
3. Distance problem 2
A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
4. Distance problem
A=(x, x) B=(1,4) Distance AB=√5, find x;
5. The publisher
The publisher prepares the release of the dictionary. Print preparation costs no matter the number of printed copies of 150000 CZK. The printer charges 80 CZK for one print. A) What are the costs of one dictionary if 5000 copies printed? B) For what num
6. Supplementary angles
One of the supplementary angles is larger by 33° than the second one. Calculate the angles size.
7. Overtaking
On the direct road, the passenger car overtakes the slower bus by starting to overtake 20 meters from the bus and after passing it ahead of it again 20 meters away. The car overtakes at a steady speed of 72 km/h, the bus goes at a steady speed of 54 km/h.
8. Paratrooper
After the parachute is opened, the paratrooper drops to the ground at a constant speed of 2 m/s, with the sidewinding at a steady speed of 1.5 m/s. Find: a) the magnitude of its resulting velocity with respect to the ground, b) the distance of his land f
9. 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 cont
10. Air thermal
Imagine that a unit of air rises at 3000 meters high, if temperature decreases 6 degrees celcius for every 1000 meter, what will be its temperature at 1400 meters, 2000 meters, 2500 meters and when it reaches the 3000 meter elevation. Starting temperature
11. Distance of lines
Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm
12. Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the
13. Find the 5
Find the equation with center at (1,20) which touches the line 8x+5y-19=0
14. Points collinear
Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
15. Two people
Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa
16. 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?
A meter pole perpendicular to the ground throws a shadow of 40 cm long, the house throws a shadow 6 meters long. What is the height of the house?
18. Two chords
There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure.
19. Prove
Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
20. Two heights and a side
Construct triangle ABC when the given side is c = 7 cm, height to side a va = 5 cm and height to side b: vb = 4 cm.

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