Line segment - practice problems - page 3 of 9
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 180
- The midpoint 2
Find the value of x if M is the midpoint of PQ, PQ=10x−7, and PM=14. - Figure 2
Figure A maps to figure B with a scale factor of 0.75. The length of the line AB segment in figure A is 10. What is its length on the image in figure B? - Polygon 3
Polygon ABCD is dilated, rotated, and translated to form polygon QWER. The endpoints A and B are at (0, -7) and (8, 8), and the endpoints QW are at (6, -6) and (2, 1.5). What is the scale factor of the dilation? - Divide line segment
Find the point P on line segment AB, such that |AP| = r |AB|. Coordinates of endpoints: A = (−2, 0, 1), B = (10, 8, 5), ratio r = 1/4. - Parallelogram perimeter construction
Assembly parallelogram ABCD: AB = 4.8 cm, va = 3 cm, BC = 4 cm. Calculate the circuit. Make a sketch. - Line ratio division
We divided line AB into two parts in a ratio of 3:5. The longer part was 6 cm longer than the shorter part. How long was the whole line in cm? - Trapezoid - construction
Construct a trapezoid ABCD (AB // CD): | AB | = 7 cm | BC | = 3.5 cm | CD | = 4 cm The magnitude of the angle ABC = 60° - Rod ratio division
How do you divide a 3 m long rod in a ratio of 1:5? Specify the length of both parts in cm. - Steel bar cutting We must cut three steel bars with 24 dm, 3 m, and 160 cm lengths into equal lengths. Find their maximum length and number.
- Line ratio enlargement
A line segment 8 cm long is enlarged in the ratio 7:4. How long in centimetres will the new segment be? - Triangle construction sides
Construct a right triangle ABC with the hypotenuse AB: a) | AB | = 72 mm, | BC | = 51 mm b) | AB | = 58 mm, | AC | = 42 mm - Segment center coordinates
The line PQ is defined by points with coordinates P = [−2; 4] and Q = [4; 0]. What are the coordinates of the midpoint S of the line segment PQ? - Dividing rod
The 3 m long rod should be divided into two parts so that one is 16 cm longer than the other. Find the lengths of both parts. - Trisection of a line segment
Divide the line segment AB into three equal parts. Instructions: Construct an equilateral triangle ABC and find its center (e.g., the described circles). - Points OPQ
Point P is on line segment OQ. Given OP = 6, OQ = 4x - 3, and PQ = 3x, find the numerical length of OQ. - The coordinates
The coordinates (5, 2) and (-6, 2) are vertices of a hexagon. Explain how to find the length of the segment formed by these endpoints. How long is the segment? - Construct 8
Construct an analytical geometry problem where it is asked to find the vertices of a triangle ABC: The vertices of this triangle are points A (1,7), B (-5,1) C (5, -11). The said problem should be used the concepts of distance from a point to a line, rati - A rope
Paul can cut a rope into equal lengths with no rope left over. The lengths can be 15 cm, 18 cm, or 25 cm. What is the shortest possible length of the rope? - Chord distance
Two parallel chords in a circle with a radius of 6 cm have lengths of 6 cm and 10 cm. Calculate their distance from each other. Find both solutions. - Parametric equation
Point A [6; -2]. Point B = [-3; 1] Write the parametric equation of the line BA so that t belongs to the closed interval < 0;3 >
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