# The image of the point (2,1) under a translation is (5,-3). Find the coordinates of the image of the point (6,6) under the same translation.

Question
Vectors and spaces
The image of the point (2,1) under a translation is (5,-3). Find the coordinates of the image of the point (6,6) under the same translation.

2020-10-22

### Relevant Questions

Suppose the vertices of the original figure in the example were A(-6,6), B(-2,5), and C(-6,2). What would be the vertices of the image after a 90° clockwise rotation about the origin?
A'()
B'()
C'(___)
Find the coordinates of T given that S is the midpoint of RT, R(2,6) and S(-2, 0).
a) To find:
The images of the following points under under a 90^circ rotation counterclockwise about the origin:
I. $$(2,\ 3)$$
II. $$(-1,\ 2)$$
III, (m,n) interms of m and n
b)To show:
That under a half-turn with the origin as center, the image of a point $$(a,\ b)\ \text{has coordinates}\ (-a,\ -b).$$
c) To find:
The image of $$P (a,\ b)\ text{under the rotation clockwise by} 90^{\circ}$$ about the origin.
For each problem below, either prove that the mapping is linear or explain why it cannot be linear.
$$\displaystyle{1}.{f{{\left({x}_{{1}},{x}_{{2}}\right)}}}={\left({2}{x}_{{1}}-{x}_{{2}},{3}{x}_{{1}}+{x}_{{2}}\right)}$$
$$\displaystyle{2}.{L}{\left({x},{y},{z}\right)}={\left({x}+{y},{y}+{z},{z}+{5}\right)}$$
$$\displaystyle{3}.{L}{\left({x},{y}\right)}={\left({x}+{y},{0},{x}-{2}{y}\right)}$$
$$\displaystyle{4}.{f{{\left({x},{y}\right)}}}={\left({2}{x}+{y},-{3}{x}+{5}{y}\right)}$$
$$\displaystyle{5}.{f{{\left({x},{y}\right)}}}={\left({x}^{{2}},{x}+{y}\right)}$$
$$\displaystyle{6}.{L}{\left({x},{y}\right)}={\left({x},{x}+{y},-{y}\right)}$$
Find the Euclidean distance between u and v and the cosine of the angle between those vectors. State whether that angle is acute, obtuse, or $$\displaystyle{90}^{{\circ}}$$. u = (-1, -1, 8, 0), v = (5,6,1,4)
Given the vector $$r(t) = { cosT, sinT, ln (CosT) }$$ and point (1, 0, 0) find vectors T, N and B at that point. $$Vector T is the unit tangent vector, so the derivative r(t) is needed. \( Vector N is the normal unit vector, and the equation for it uses the derivative of T(t). \( The B vector is the binormal vector, which is a crossproduct of T and N. asked 2021-02-08 Determine the area under the standard normal curve that lies between ​ (a) Upper Z equals -2.03 and Upper Z equals 2.03​, ​(b) Upper Z equals -1.56 and Upper Z equals 0​, and ​(c) Upper Z equals -1.51 and Upper Z equals 0.68. ​ ​(Round to four decimal places as​ needed.) asked 2020-11-10 Describe the translation of figure ABCD. Use the drop-down menus to explain your answer. Figure ABCD is translated _____ unit(s) right and ______ unit(s) up. asked 2020-11-20 Find the angles made by the vectors \(\displaystyle{A}={5}{i}-{2}{j}+{3}{k}$$ with the axes give a full correct answer
Find all scalars $$c_{1} , c_{2}, c_{3}$$ such that $$c_{1}(1 , -1, 0) + c_{2}(4, 5, 1) + c_{3}(0, 1, 5) = (3, 2, -19)$$