What are the new coordinates of the point (18, 8) under the dilation (x, y) → (1.5x, 1.5y)? O (32, 12) O (27, 12) O (27, 16) O (18, 12)

Q: Calculate û x ô if û = ĵ + 2k and û = -i - ĵ + k. %3D

A: Topic = Vector   if u→ =a1i+a2j+a3k and v→ =b1i+b2j+b3kthenu→×v→=ijka1a2a3b1b2b3

Q: What is the coordinates of P₁ if (1,-2,8) is the midpoint between P₁(x1,1,Z1) and P2(-4,5,6)?…

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Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: Suppose XY has coordinates X( -2, 5) and Y(3, -9). What are the coordinates for the midpoint of XY?

A: To find the Midpoint of the line.

Q: 9 Find the distance from the point (-7,-3,4) to the xy-plane.

A: Distance of a point (a,b,c) from the plane lx+my+nz=p is (la+mb+nc-p)/sqrt(l^2+m^2+n^2)

Q: Find the point on y = 4+ x² that is closest to (1, 1). 0 (0,4) O (0.142, 4.020) O (0.545, 4.194) O…

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Q: What are the coordinates of C' after its preimage, C(5,-3), is reflected over the x-axis? O (5,3) O…

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Q: Translate Q (0, -8) using (x, y) → (x - 3, y+ 2). Your answer: O Q'(-2, 5) Q' (3, - 10) O Q'(-3, -6)…

A: The transformation is, (x,y) ------> (x-3, y+2) So, (0, -8) ------> (0-3, -8+2)

Q: Let Ax,y) = 5x + 5xy – 6y. Give the coordinates of a point on the graph of f at the point (3,6). O…

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Q: Find the distance between 4y + 3x = 4 and point (0, 5) O 3.4 O 3.2 O 2.8 3

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Q: Calculate fx(l, 3) and /y(l, 3) for f (x, y) =

A: Given: fx,y=7x+y2

Q: Rotate the point (2,5) by (3/5,4/5) around origin (0,0).

A: Given:  point A2,5Rotate by 35,45 around origin 0,0.…

Q: Calculate the length of PQ where P = (-2,1,6) and Q = (-3,4, –1).

A: We will find the length of PQ→ in the following step

Q: Let C1 be the line segment from (1,0,1) to (0,3,6). Evaluate dx + dy + dz.

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Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

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Q: What is the distance between the points M(-3,1) and N(7,-3)?

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Q: Identify the rule for this Translation (x+-, y+–) Coordinates Preimage Image A (2,4) A B A' B' C D…

A: To find the translation

Q: Find the distance d between the points (1, 3) and (5, 6).

A: Our Aim is to find the distance between the points (1,3) and (5,6).

Q: Use Linear Approximation to estimate the change, Az, in z = 8x2 + y? as (x, y) changes from (2, 3)…

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Q: 16. Where does the smallest value f(r, y) + 3ay + y occur on the rectangle (-2, 2) x (-3, 1]? a) It…

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Q: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…