In Exercises 41-44, find the intersection of the line and the plane.43. z = 12, r(t) = t (-6, 9, 36)

Q: 11. Determine whether the lines are parallel, perpendicular, or neither. Show your work. 4 Line 1:…

A: Since the product of slopes is -1 hence these lines are perpendicular.

Q: Find the angles between the planes x + y = 1, 2x + y - 2z = 2

A:

Q: A quadrilateral has coordinates R(-5,2),S(-1,3), T(-2,–1) and U(-6,– 2). Verify algebraically, that…

A: Let X be mid point of R(-5,2) and S(-1,3) ∴Coordinate of X is -5-12,2+32…

Q: One endpoint of a line segment has coordinates represented by (+6, y). The midpoint of the line…

A:

Q: In Exercises 25–30, find the distance between points P1 and P2. 25. P1(1, 1, 1), P2(3, 3, 0) 26.…

A: Given,

Q: 9 What is the distance between points (-10, 6) and (-2, 2) on a coordinate plane?

A:

Q: Sketch the translation of the triangle with the rule (x, y) → (x+5, y+1). T 5 -10 -5 5 10 --5

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Q: Find the intersection point of the two lines: [x, y, z] = [–2, 3, –3] + t[1, –1, 2] and [x, y, z]…

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Q: ais the midpoint of AB. Q has coordinates of (-2, 4) and A has coordinates of (4,6). What are the…

A: Solution of the problem as follows

Q: Find the distance from the point to the plane.   (4,1,8)​, 7y+5z=0

A:

Q: R: square with vertices (0, 0), (2, 0), (0,

A: Given,         f(x, y)=19+3x-3y         R: square with vertices (0, 0), (2, 0), (0, 2), (2, 2).

Q: What is the distance between points (5, 2) and (1, -3) on a coordinate plane? 4.1 © 8.5 6.4

A: We can use distance formula to find distance between two points (x1,y1) and (x2,y2).

Q: Find a plane containing the point (– 3, – 3, 7(t) = (– 2, – 3, – 5) + t(3, 4) and the line 6, 7).

A: we have to find the equation of plane that contains the point (-3,-3,-4)  and the line…

Q: etermine the intersection point of the two lines or show that they do not intersect. a. Does the…

A: Given: (-5,4,-1) and (-3,-5,0)

Q: n Exercises 39–41, find the distance from the point to the plane. 39. (2, 2, 3), 2x + y + 2z = 4 40.…

A: Given:

Q: Is Span({(4,–10, 6), (-6, 15,–9)}) a line or a plane in R³? Why?

A:

Q: In space coordinates system, the y-axis consists of all points of the form O (x, 0, 0) O (0, 0, z) O…

A: we know that(x,y,z) is nothing but distace of a point from origin along the x,y,z-axis

Q: Find the point of intersection of the line through (1, -4, 1) and (4, -12, 6), and the plane given…

A: Find equation of line and put parametric value of (x,y,z) in plane and solve for x,y and z.

Q: In Exercises 33–34, find the distance from the point to the line. 33. (2, 1, 3); x = 2 + 2t, y = 1 +…

A: Since we only answer up to 1 question, we’ll answer the first question. Please resubmit the question…

Q: The plane that passes through  (9, 0, −3)  and contains the line  x = 6 − 3t, y = 2 + 5t, z = 4 +…

A: Given : A point (9,0,-3) where the plane passes through.             A system of equations for line…

Q: The point (5,4,7) is the midpoint between the points (10,8,1) and (x,y,2). Find (x,y,2).

A:

Q: Find the areas of the parallelograms whose vertices are given in Exercises 35–40. 35. A(1, 0), B(0,…

A: Area of parallelogram ABCD is |AB x AD|

Q: What is 8,9 reflected over y-axis

A: The point (8,9) is shown in the graph,

Q: Use analytic geometry to classify the quadrilateral with vertices J(-2,1), K(2, 3), L(4, -1), and…

A: We have to classify the quadrilateral

Q: Find the point of intersection of the line through (1, -5, 1) and (5,-12, 6), and the plane given by…

A: we know that equation of line which passes through two pointsx1,y1,z1,x2,y2,z2 is given by…

Q: Find the point on the plane −2 x+y−z =−9 that is closest to the point (3,−2,2) .

A: We have to find a point on the plane closest to another point.

Q: One endpoint of a line segment has coordinates represented by (x + 2, y). The midpoint of the line…

A:

Q: In Exercises 33–34, find the distance from the point to the line. 33. (3, -1, 4); x = 4 - t, y = 3 +…

A: Note:We’ll answer the 33th question since we answer only one question at a time. Please submit a new…

Q: 2. Obtain an equation for a plane 7 that includes straight line(2"--5) and point(-2,1,1).

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Q: 6. parallel to y%3D through (-3, 6)

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Q: What is the midpoint of line segment XY with coordinates X (-4, 10) and Y (8,6)? (-6, 2) (3, 7) (-7,…

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Q: In Exercises 33–34, find the distance from the point to the line. 33. (0, 0, 12); x = 4t, y =-2t, z…

A: We’ll answer the 33th question since we answer only one question at a time. Please submit a new…

Q: n Exercises 39–41, find the distance from the point to the plane. 39. (2, -3, 4), x + 2y + 2z = 13…

A: Given, (2, -3, 4), x + 2y + 2z = 13.

Q: Describe the plane x = 4.

A: Given, plane x=4we have to describe the plane x=4

Q: Find the point of intersection of the line through (1, -5, 1) and (5, -12, 6), and the plane given…

A:

Q: What is the image of the triangle shown after a translation with the rule (x, y)→ (x-3, y+3)? 8 4 -4…

A: Given: The rule for the translation is x, y→x-3, y+3.

Q: In Exercises 41-44, find the intersection of the line and the plane.42. 2x + y = 3, r(t) = (2, -1,…

A: Given: To find the intersection of the line and the plane.2 x + y = 3,  r(t) = (2, -1, -1) + t (1,2,…

Q: The coordinates of the midpoint of line AB are (2,4). and B (3,7). What are the coordinates of A?

A: Here given as The coordinates of the midpoint of line AB are (2,4). and B (3,7). Let coordinate of A…

Q: 3. What are the three possibilities for the intersection of a line and a plane?

A: The solution is given in the next step.

Q: 6. The midpoint of a line segment in the standard (x,y) coordinate plane is (–5, 8). If one endpoint…

A: The midpoint of a line segment in the standard x, y coordinate plane is -5, 8. If one endpoint of…

Q: How to find an equation of a plane through a specific point such as (3,0,3)?

A: There can be infinitely many planes passing through one point and hence you can not find an equation…

Q: Represent two planes that intersect at a line represented by 3 +2

A: There are so many pair of planes that represents the same line.

Q: The line passes through the point(7, 8, 9) and is parallel to the xz-plane and the yz-plane. 7,8,1 +…

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Q: Where does the line through (1, 0, 1) and (3, –3, 4) intersect the plane x + y + z = 6? (x, y, z) =…

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Q: 5, what is the speed of the plane?

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Q: 6. JaMarcus claims that (2,1) is the point of intersection of the lines y = 5x-3 and y=-4x+6. Is he…

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Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

A: Given : the equation of a plane is  x-y+z=5  and the line passes through (1, -4, 1)  and (4, -10,…

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -8, 4), and the plane given by…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.