The point A has coordinates (3,1) and the point B has coordinates (-21, 11). The point...
The point A has coordinates (3,1) and the point B has coordinates (-21, 11). The point C is the midpoint of AB.
(i) Find the equation of the line through A that is perpendicular to y = 2x -7
(ii) Find the distance AC
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The point A has coordinates (3,1) and the point B has
coordinates (-21, 11). The point...
B (2,4) A (-2,3) C (11,2) 0 3y+ 2x+5-0 In the diagram, the points A, Band C have coordinates (-2,3), (2,4) and (11,2) respectively. D is a point such that DA is perpendicular to AB, and Dlies on...
B (2,4) A (-2,3) C (11,2) 0 3y+ 2x+5-0 In the diagram, the points A, Band C have coordinates (-2,3), (2,4) and (11,2) respectively. D is a point such that DA is perpendicular to AB, and Dlies on the line 3y+ 2x+ 5 = 0. 141 Find the coordinates of D. Point E lies on DC and the ratio of the length of DE to the length of DCis 2:3 (i) 141 (ii) Find the area of triangle DBE. (ii)...
A is the point (-1, 5). Let (x, y) be any point on the line y = 3x.
A is the point (-1, 5). Let (x, y) be any point on the line y = 3x. a Write an equation in terms of x for the distance between (x, y) and A(-1,5). b Find the coordinates of the two points, B and C, on the line y = 3x which are a distance of √74 from (-1,5). c Find the equation of the line l1 that is perpendicular to y = 3x and goes through the point (-1,5). d Find the coordinates...
Please show work on how to get the answers. Thanks in advance! :) 7. Let P(-3,1)and...
Please show work on how to get
the answers. Thanks in advance! :)
7. Let P(-3,1)and Q(5.6) be two points in the coordinate plane. (a) Find the distance between P and Q (b) Find the midpoint of the segment Po. (c) Find the slope of the line that contains P and Q d) Find an equation of the line in standard form that contains P and 0 (e) Find an equation of the line in standard form that is perpendicular...
Question 4 g A-2 B 6 0 The sketch shows a circle, a parabola, which is...
Question 4 g A-2 B 6 0 The sketch shows a circle, a parabola, which is the graph of f, and a straight line, which is the graph of g. The parabola has x-intercepts –2 and 6, and y-intercept 6. Its turning point is C. The circle has its centre at the origin and it passes through the point A, which has coordinates (-2,0). At point B both the circle and the straight line cut the x-axis. The straight line...
hlep me these 2 t, 3- 3 and (-2r, 3-, ) 11.) Determine the point of...
hlep me these
2 t, 3- 3 and (-2r, 3-, ) 11.) Determine the point of intersection of the lines Note:4,1,2, with (1,2/3,-1)^k(-2.-1,1)=kv;, for any kER. So .1,. Change one of the parameters to s, then equate the corresponding coordinates of the lines and solve for t, and s. substitute the values of t, and s in their respective lines to get the required point. Locate the point of intersection of the plane 2x+ y-z-0 and the line through (3,1,0)...
Give a geometric description of the set of points whose coordinates satisfy the given conditions. 1)...
Give a geometric description of the set of points whose coordinates satisfy the given conditions. 1) X-5-4 A) All points in the x-z plane B) The line through the point (5.0,-4) and parallel to the y-axis C) The line through the point (5. -4,0) and parallel to the z-axis D) The point (5.-4) Describe the given set of points with a single equation or with a pair of equations. 2) The plane perpendicular to the y-axis and passing through the...
B and D Sum of cubes: a³ + b³ = (a + b)(a² – ab +...
B and D
Sum of cubes: a³ + b³ = (a + b)(a² – ab + b²) Difference of cubes: a3 - b -btVb?-4ac -by Vertex formula: f ) Quadratic formula: x = 2a 2a Y2 - Y1 X2 - X1 y = mx + b т3 1) Find the slope-intercept form of the line satisfying the following conditions Perpendicular to y =x and passing through the point (7, 5) a. b. Parallel to 2x - 7y = -24 and...
B. Distance from a point to a plane: We'll give a general formula Monday in class....
B. Distance from a point to a plane: We'll give a general formula Monday in class. The steps below present an alternative (more geometric) approach. (3) Given the plane II: 2x – y +3z = 1 and the point P(1,2, -4), find the distance between P and II as follows: (i) Find the vector or parametric equations for the line L that contains P and is perpendicular to II . (ii) Find the point of intersection Q of the plane...
Determine the following: (A) The angle formed by cables AB and AD (B) The perpendicular distance...
Determine the following: (A) The angle formed by cables AB and AD (B) The perpendicular distance from point B to the line AD (C) If the force in cable AC is 500N, find the component of that force in the direction of line AB If the force in cable AC is 500N, find the moment of this force about a line joining BD (D) What is the perpendicular distance from point B and cable AC? (E) 0.36 m 0.56 m...
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d =...
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d = 0 C(0, -2,1). Put the plane equation B(3,1, 0) х — 3 z+2 = y+5 = 2 L: Find the intersection point between 2 lines whose symmetric equations are: 4 х-2 L, : у-2 = z-3 -3 Find the parametric equation for a line that is going through point A(2,4,6) and perpendicular to the plane 5х-3у+2z-4%3D0. Name: x-3y4z 10 Find the distance between 2...
B (2,4) A (-2,3) C (11,2) 0 3y+ 2x+5-0 In the diagram, the points A, Band C have coordinates (-2,3), (2,4) and (11,2) respectively. D is a point such that DA is perpendicular to AB, and Dlies on the line 3y+ 2x+ 5 = 0. 141 Find the coordinates of D. Point E lies on DC and the ratio of the length of DE to the length of DCis 2:3 (i) 141 (ii) Find the area of triangle DBE. (ii)...
Please show work on how to get
the answers. Thanks in advance! :)
7. Let P(-3,1)and Q(5.6) be two points in the coordinate plane. (a) Find the distance between P and Q (b) Find the midpoint of the segment Po. (c) Find the slope of the line that contains P and Q d) Find an equation of the line in standard form that contains P and 0 (e) Find an equation of the line in standard form that is perpendicular...
Question 4 g A-2 B 6 0 The sketch shows a circle, a parabola, which is the graph of f, and a straight line, which is the graph of g. The parabola has x-intercepts –2 and 6, and y-intercept 6. Its turning point is C. The circle has its centre at the origin and it passes through the point A, which has coordinates (-2,0). At point B both the circle and the straight line cut the x-axis. The straight line...
hlep me these
2 t, 3- 3 and (-2r, 3-, ) 11.) Determine the point of intersection of the lines Note:4,1,2, with (1,2/3,-1)^k(-2.-1,1)=kv;, for any kER. So .1,. Change one of the parameters to s, then equate the corresponding coordinates of the lines and solve for t, and s. substitute the values of t, and s in their respective lines to get the required point. Locate the point of intersection of the plane 2x+ y-z-0 and the line through (3,1,0)...
Give a geometric description of the set of points whose coordinates satisfy the given conditions. 1) X-5-4 A) All points in the x-z plane B) The line through the point (5.0,-4) and parallel to the y-axis C) The line through the point (5. -4,0) and parallel to the z-axis D) The point (5.-4) Describe the given set of points with a single equation or with a pair of equations. 2) The plane perpendicular to the y-axis and passing through the...
B and D
Sum of cubes: a³ + b³ = (a + b)(a² – ab + b²) Difference of cubes: a3 - b -btVb?-4ac -by Vertex formula: f ) Quadratic formula: x = 2a 2a Y2 - Y1 X2 - X1 y = mx + b т3 1) Find the slope-intercept form of the line satisfying the following conditions Perpendicular to y =x and passing through the point (7, 5) a. b. Parallel to 2x - 7y = -24 and...
B. Distance from a point to a plane: We'll give a general formula Monday in class. The steps below present an alternative (more geometric) approach. (3) Given the plane II: 2x – y +3z = 1 and the point P(1,2, -4), find the distance between P and II as follows: (i) Find the vector or parametric equations for the line L that contains P and is perpendicular to II . (ii) Find the point of intersection Q of the plane...
Determine the following: (A) The angle formed by cables AB and AD (B) The perpendicular distance from point B to the line AD (C) If the force in cable AC is 500N, find the component of that force in the direction of line AB If the force in cable AC is 500N, find the moment of this force about a line joining BD (D) What is the perpendicular distance from point B and cable AC? (E) 0.36 m 0.56 m...
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d = 0 C(0, -2,1). Put the plane equation B(3,1, 0) х — 3 z+2 = y+5 = 2 L: Find the intersection point between 2 lines whose symmetric equations are: 4 х-2 L, : у-2 = z-3 -3 Find the parametric equation for a line that is going through point A(2,4,6) and perpendicular to the plane 5х-3у+2z-4%3D0. Name: x-3y4z 10 Find the distance between 2...
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