Geometry Problems on a Coordinate Plane Geometry Analytic Geometry Geometry Problems on a Coordinate Plane Questions What is the definition of a coordinate proof? And what is an example? How would you do coordinate geometry proofs? What is the slope of the line through P(6, −6) and Q(8, −1)? Find the slope of the line through P(−5, 1) and Q(9, −5)? What is the slope of the line through P(2, 8) and Q(0, 8)? What is the an equation of the line that goes through (−1, −3) and is perpendicular to the line 2x + 7y + 5 = 0? What is an equation of the line that goes through point (8, −9) and whose slope is undefined? Given two ordered pairs (1,-2) and (3,-8), what is the equation of the line in slope-intercept form? How would you solve the system of these two linear equations: 2x + 3y = -1 and x - 2y = 3? Enter your solution as an ordered pair (x,y). Which of the ordered pairs forms a linear relationship: (-2,5) (-1,2) (0,1) (1,2)? Why? What is the radius of a circle given by the equation (x+1)^2+(y-2)^2=64? Find the vertex and axis of symmetry of this: y = -3 (x + 4)^2 +2? What is the line of intersection between the planes 3x+y-4z=2 and x+y=18? How do you find the angle between the planes x + 2y - z + 1 = 0 and x - y + 3z + 4 = 0? Can two lines (each on a different plane) intersect? Are the planes x+y+z=1 , x-y+z=1 parallel, perpendicular, or neither? If neither, what is the angle between them? What is the distance between the planes 2x – 3y + 3z = 12 and –6x + 9y – 9z = 27? How do you determine if two vectors lie in parallel planes? How do I calculate the distance between the two parallel planes x - 2y + 2z = 7 and 2y - x - 2z = 2? How can planes intersect? What are the parametric equations for the line of intersection of the planes x + y + z = 7 and x + 5y + 5z = 7? How do I find the angle between the planes x + 2y − z + 1 = 0 and x − y + 3z + 4 = 0? What are the equations of the planes that are parallel to the plane x+2y-2z=1 and two units away from it? Find the intersection point between x^2+y^2-4x-2y=0 and the line y=x-2 and then determine the tangent that those points? Question #ed0b6 Question #6de4a Let M be a matrix and u and v vectors: M =[(a, b),(c, d)], v = [(x), (y)], u =[(w), (z)]. (a) Propose a definition for u + v. (b) Show that your definition obeys Mv + Mu = M(u + v)? Let M and N be matrices , M = [(a, b),(c,d)] and N =[(e, f),(g, h)], and v a vector v = [(x), (y)]. Show that M(Nv) = (MN)v? Given C_1->y^2+x^2-4x-6y+9=0, C_2->y^2+x^2+10x-16y+85=0 and L_1->x+2y+15=0, determine C->(x-x_0)^2+(y-y_0)^2-r^2=0 tangent to C_1,C_2 and L_1? Given L_1->x+3y=0, L_2=3x+y+8=0 and C_1=x^2+y^2-10x-6y+30=0, determine C->(x-x_0)^2+(y-y_0)^2-r^2=0 tangent to L_1,L_2 and C_1? The equations {(y = c x^2+d, (c > 0, d < 0)),(x = a y^2+ b, (a > 0, b < 0)):} have four intersection points. Prove that those four points are contained in one same circle ? What are two lines in the same plane that intersect at right angles? Given the surface f(x,y,z)=y^2 + 3 x^2 + z^2 - 4=0 and the points p_1=(2,1,1) and p_2=(3,0,1) determine the tangent plane to f(x,y,z)=0 containing the points p_1 and p_2? What is the equation of the line passing through (-3,-2 ) and (1, -5)? How do we find out whether four points A(3,-1,-1),B(-2,1,2), C(8,-3,0) and D(0,2,-1) lie in the same plane or not? If the planes x=cy+bz , y=cx+az , z=bx+ay go through the straight line, then is it true that a^2+b^2+c^2+2abc=1? How to determine the coordinates of the point M?A_(((2,-5)));B_(((-3,5)));And vec(BM)=1/5vec(AB) Question #50ea4 Is my teacher's final answer wrong? Analytic Geometry View all chapters Geometry Problems on a Coordinate Plane Distance between Points Equations of Parallel and Perpendicular Lines Next