Triangle + analytic geometry - practice problems - page 5 of 6
Number of problems found: 109
- Coefficient 81704
In the equation of the line p: ax-2y+1=0, determine the coefficient a so that the line p: a) it formed an angle of 120° with the positive direction of the x-axis, b) passed through point A[3,-2], c) was parallel to the x-axis, d) had a direction of k = 4. - Prove
Prove that k1 and k2 are 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 - Right angled triangle 2
LMN is a right-angled triangle with vertices at L(1,3), M(3,5), and N(6,n). Given angle LMN is 90° find n - Quadrilateral 47493
A regular quadrilateral prism ABCDEFGH has a base edge A B 8 cm long and 6 cm high. Point M is the center of the edge AE. Determine the distance of point M from the BDH plane.
- Three points
Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is the value of k? - Calculate 82992
Given cuboid ABCDEFGH. We know that |AB| = 1 cm, |BC| = 2 cm, |AE| = 3 cm. Calculate in degrees the angle size formed by the lines BG and FH . - Vertices of a right triangle
Show that the points D(2,1), E(4,0), and F(5,7) are vertices of a right triangle. - 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 /. - The triangle
Three vertices give the triangle: A [0.0] B [-4.2] C [-6.0] Calculate V (intersection of heights), T (center of gravity), O - the center of a circle circumscribed
- Ellipse
Ellipse is expressed by equation 9x² + 25y² - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the ellipse's center. - Right triangle from axes
A line segment has its ends on the coordinate axes and forms 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? - Four sides of trapezoid
The trapezoid is given by the length of four sides: 40.5 42.5 52.8 35.0. Calculate its area. - Ladder
A 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Center of line segment
Calculate the distance of point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t; t is from interval <0,1>.
- Coordinates of a centroind
Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians). - Calculate 4865
Calculate the length of the line segment AB, given A [8; -6] and B [4; 2] - Distance
Calculate the distance between two points K[6; -9] and G[5; -1]. - Midpoint of segment
Find the distance and midpoint between A(1,2) and B(5,5). - Center
In the ABC triangle is point D[1,-2,6], which is the center of the |BC|, and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
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