Analytic geometry + Pythagorean theorem - practice problems
Number of problems found: 101
- 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. - 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? - Triangle 82
Triangle PQR has vertices located at (2, 2), (5, -4), and (-4, -1). What type of triangle is triangle PQR? - Line segment
Find the length of the line joining points A(-4,8) and B(-1,4).
- 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| - Calculate 83160
Calculate the distance of point A[ 4; 2; -3 ] from the plane : 2x - 2y + z + 5 = 0 - Circle - analytics geometry
Write the equation of the circle that passes through the points Q[3.5] R[2.6] and has its center on the line 2x+3y-4=0. - Calculate 82578
The vertices of triangle ABC are: A[1, 2, -3], B[0, 1, 2], C[2, 1, 1]. Calculate the lengths of sides AB, AC and the angle at vertex A. - 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]
- Determine 82478
Determine the equation of the parabola that has the point F = [3,2] as its focus and the line x+y+1=0 as its shift line. - Determine 82394
Determine the equation of the circle that passes through the point M(-1,2) and N( 3,0) and whose center lies on the line p: x=-3+t, y=-1+t, - Determine 82341
Determine the equation of the circle that is the set of all points of the plane that are twice as far from the point [3,7] as they are from the point [0,1]. - Calculate 82144
Calculate the height of side b (v_b) of triangle ABC with vertices A[4;1;3] B[2;3;3] and C[1;1;3]. - Equation 81932
Write the general equation of a circle with point S(2;5) and point B(5;6) lying on this circle.
- X-coordinate 81737
In triangle ABC, determine the coordinates of point B if you know that points A and B lie on the line 3x-y-5=0, points A and C lie on line 2x+3y+4=0, point C lies on the x-coordinate axis, and the angle at vertex C is right. - Equation of the circle
Find an equation of the circle whose diameter has endpoints (1,-4) and (3,2). - Crosswind
A plane is traveling 45 degrees N of E at 320 km/h when it comes across a current from S of E at 115 degrees of 20 km/h. What are the airplane's new course and speed? - The coordinates 2
The coordinates of the vertices of the triangle shown are A(1,7), B(5,2), and C(5,7). What is the length of segment AB in units? - Quadrilateral PQRS
PQRS is a quadrilateral with P(4,4), S(8,8), and R(12,8). If vector PQ=4*vector SR, find the coordinates of Q. Solve it
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