# Geometry - math word problems

#### Number of problems found: 324

- Proportional relationship

The ordered pairs (6,24) and (1, s) represent a proportional relationship. Find the value of s. - Perpendicular projection

Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0. - Ascend vs. descent

Which function is growing? a) y = 2-x b) y = 20 c) y = (x + 2). (-5) d) y = x-2 - A cliff

A line from the top of a cliff to the ground passes just over the top of a pole 5 ft high and meets the ground at a point 8 ft from the base of the pole. If the point is 93 ft from the base of the cliff, how high is the cliff? - General line equations

In all examples, write the GENERAL EQUATION OF a line that is given in some way. A) the line is given parametrically: x = - 4 + 2p, y = 2 - 3p B) the line is given by the slope form: y = 3x - 1 C) the line is given by two points: A [3; -3], B [-5; 2] D) t - Coordinates of the intersection of the diagonals

In the rectangular coordinate system, a rectangle ABCD is drawn. The vertices of the rectangle are determined by these coordinates A = (2.2) B = (8.2) C = (8.6) D = (2.6) Find the coordinates of the intersection of the diagonals of the ABCD rectangle - There

There is a triangle ABC: A (-2,3), B (4, -1), C (2,5). Determine the general equations of the lines on which they lie: a) AB side, b) height to side c, c) Axis of the AB side, d) median ta to side a - Isosceles triangle

In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C. - Vertical rod

The vertical one meter long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long at the same time. - Poplar shadow

The nine-meter poplar casts a shadow 16.2 m long. How long does a shadow cast by Peter at the same time, if it is 1.4 m high? - Chimney and tree

Calculate the height of the factory chimney, which casts a shadow 6.5 m long in the afternoon. At the same time, a 6 m high tree standing near it casts a shadow 25 dm long. - Similar triangles

Triangle A'B'C 'is similar to triangle ABC, whose sides are 5 cm, 8 cm, and 7 cm long. What is the length of the sides of the triangle A'B'C ' if its circumference is 80 cm? - Line intersect segment

Decide whether the line p : x + 2 y - 7 = 0 intersects the line segment given by points A[1, 1] and B[5, 3] - Find the 13

Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3] and C[9, 4]. - The triangles

The triangles ABC and A'B'C 'are similar with a similarity coefficient of 2. The angles of the triangle ABC are alpha = 35°, beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '. - Vector v4

Find the vector v4 perpendicular to vectors v1 = (1, 1, 1, -1), v2 = (1, 1, -1, 1) and v3 = (0, 0, 1, 1) - Two ribbons

The total length of the two ribbons is 13 meters. If one ribbon is 7 and 5/8 meters long, what is the length of the other ribbon? - Calculate 6

Calculate the distance of a point A[0, 2] from a line passing through points B[9, 5] and C[1, -1]. - Similar triangles

In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D´E´F´ is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D´E´F´ if the similarity coefficient is one-seventh. - Similarity coefficient

In the triangle TMA the length of the sides is t = 5cm, m = 3.5cm, a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other.

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