(part 1 of 4) Suppose you start at the origin in 3-space, move along the x-axis a distance of 2 units in the positive direction, and then move down- ward a distance of 3 units. What are the coordinates of your position? 1. (2,0, -3) 2. (2, -3,0) 3. (2,0,3) 4. (0, 2, -3) 5. (0, -3,2) (part 2 of 4) Which one of the points P(6, 9, -3), Q(8, -2, -8), R(-5, 8, 1) in 3-space is closest to the xz-plane? 1. R(-5, 8, 1) 2. P(6, 9, -3) 3. Q(8, -2, -8) (part 3 of 4) A rectangular box is constructed in 3-space with one corner at the origin and other ver- tices at (1,0,0), (0,3,0), (0, 0, 2). Find the length of the diagonal of the box. 1. length 2. length 3. length = 14 - = √22 √14 √19 4. length 5. length = 19 6. length = 22 (part 4 of 4) What are the coordinates of the projection of the point Q(-4, 5, 3) onto the zx-plane? 1. (-4, 0, 3) 2. (-4, -5, 3) (4, 5, 3) 3. 4. (-4, 5, 0) 5. (-4, 5, -3) 6. (0,5, 3)

Q: Parallel to y + 8x = 4, through (3, 4); slop- intercept form

A: The line is parallel to y+8x=4, passes through 3, 4

Q: The midpoint between the points (6, -7, -2) and(-2, 1, 4) is

A: The solution of the problem is given in the next step.

Q: 2 A -3 -1 -1 -2 The midpoint of AB = ([ ? ], [ ])

A:

Q: Directions: Transform the following equations into standard form.   10. x^2 - 3x = -2   11. y^2…

A:

Q: 2) Find the Cartesian coordinates of the following : Зл. -), (5,7) ,(10,5) , (3.5) , (-2, 5) , (4.-)…

A:

Q: (5, 0) (-2,-5)

A:

Q: Find distance between a = (3, -1, 0, -3) and b = (4, 0, 1, 2).

A: Given a=(3,-1,0,-3) and b=(4,0,1,2) and we have to find distance between a and b

Q: 4. (0, 0), (4, 3) 5. (0,-7), (5, 5) 6. (4, 2). (-1, 5) 7. (-5, 6). (-7,-2) 8. (-1,-3), (9, 0) 9.…

A:

Q: Find the distance between the two points. 4. (0, 0), (4, 3) 5. (0,-7), (5, 5) 6. (4, 2), (-1, 5) 7.…

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Q: (-1,-3), (9, 0) 9. (-4,-4), (-1,-1)

A: we knew that distance between two points (x1,x2) and (y1,y2) are  x1-y12+x2-y22. so 8. distance…