Planimetrics + analytic geometry - practice problems
Number of problems found: 157
- A triangle 10
A triangle has vertices at (4, 5), (-3, 2), and (-2, 5). What are the coordinates of the vertices of the image after the translation (x, y) arrow-right (x + 3, y - 5)? - Three 237
Three vertices of a rectangle have the coordinates (5, 3), (5, -1), (-1, -1). What are the coordinates of the fourth vertex of the rectangle? - Find all 2
Find all the complex solutions (write the answer in the form x+iy) of the system. {|z-12|/|z-8i|=5/3 ; |z-4|=|z-8| - Triangle 82
Triangle PQR has vertices located at (2, 2), (5, -4), and (-4, -1). What type of triangle is triangle PQR?
- The coordinates 3
The coordinates of two vertices of an equilateral triangle are (1,1) and (5,1). What are the coordinates of the third vertex? - Line segment
Find the length of the line joining points A(-4,8) and B(-1,4). - Coordinates - rectangle
Find the perimeter of the rectangle with vertices A(1,4), B (1,0 ), C (4,0), D (4,4 ) - A boy 5
A boy starts at A and walks 3km east to B. He then walks 4km north to C. Find the bearing of C from A. - Trigonometric fx
When an acute angle φ is in the standard position, its terminal side passes through point P (1,3). Find trigonometric functions of angle θ : sin φ, cos φ, tan φ, cotan φ.
- Luiza
Luiza delivers newspapers in her neighborhood. If you plot the points (-1, 1), (4, 1), (4, -2), and (-1, -2), you will create a representation of the route she takes in miles. How many miles does her route cover? - Quadrilateral 2
Show that the quadrilateral with vertices P1(0,1), P2(4,2), P3(3,6) P4(-5,4) has two right triangles. - Three points
Three points K (-3; 2), L (-1; 4), M (3, -4) are given. Find out: (a) whether the triangle KLM is right b) calculate the length of the line to the k side c) write the coordinates of the vector LM d) write the directional form of the KM side e) write the d - Determine 44221
For circles k1 (S1,4cm) and k2 (S2,3cm) and it holds that | S1S2 | = 8cm. Determine the distance between the circles K1 and K2. - 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?
- Parametric form
Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. - Right-angled 82561
Determine point C so that triangle ABC is right-angled and isosceles with hypotenuse AB, where A[4,-6], B[-2,10] - Intersection 3486
The rectangular coordinate system has a point A [-2; -4] and a point S [0; -2]. Determine the coordinates of points B, C, and D so that ABCD is a square and S is the intersection of their diagonals. - Determine
Determine which type of quadrilateral ABCD is and find its perimeter if you know the coordinates of vertices: A/2,4 /, B / -2,1 /, C / -2, -2 /, D/2, -5 /. - Add vector
Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
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