Planimetrics + analytic geometry - practice problems - page 7 of 8
Number of problems found: 157
- Two people
Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walks at the rate of 4 kph on one road, and Jenelyn walks at the rate of 8 kph on the other road. How long will it take for them to be 20√5 km apa - The tangent line
Find the tangent line of the ellipse 9x² + 16y² = 144 with slope k = -1. - The tangent of the hyperbola
Write the equation of the tangent of the hyperbola 9x²−4y²=36 at the point T =[t1,4]. - Coordinates hexagon
The regular hexagon ABCDEF is given. Point A has coordinates [1; 3], and point D has coordinates [4; 7]. Calculate the sum of the coordinates of the center of its described circle.
- The triangle 5
The triangle below has vertices A(-1,-2), B(2,2), and C(-1,4). What is the area of △ABCin square coordinate units? - 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). - Hyperbola
Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6]. - Coordinates 66474
Draw a trapezoid in the coordinate system with bases 4cm long, 2cm long, and 3cm high. Please write down the coordinates of its vertices. - Center
Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[-17,9] B[-26,-19] C[-7,7].
- 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>. - Vertex points
Suppose the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area. - Coordinates of the intersection of the diagonals
In the rectangular coordinate system, a rectangle ABCD is drawn. These coordinates determine the vertices of the rectangle. 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. - Coordinates 32183
The triangle ABC is given in the plane. A (-3,5), B (2,3), C (-1, -2) write the coordinates of the vectors u, v, w if u = AB, v = AC, and w = BC. Enter the coordinates of the centers of the lines SAB (..), SAC (...), SBC (. ..) - 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
- Midpoint of segment
Find the distance and midpoint between A(1,2) and B(5,5). - Lengths of medians from coordinates
There is a triangle ABC: A [-6.6; 1.2], B [3.4; -5.6], C [2.8; 4.2]. Calculate the lengths of its medians. - 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 - Triangle
Plane coordinates of vertices: K[19, -4] L[9, 13] M[-20, 8] give Triangle KLM. Calculate its area and its interior angles. - 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.
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