Translation T maps point (4, -1).What is the image of point (-1,3) under translation T?

Translation T maps point (4, -1).What is the image of point (-1,3) under translation T?
Translations 2 Name: Date: 10 Translation T maps point (26) to point (4,-1). What is the image of point (-1,3) under translation T? A translation maps P(3,-2) to P'(1, 1). Under the same translation, find the coordinates of ', the image of e-3,2) 11 A translation maps P(4, 1) to P '(2. - 1). What are the coordinates of Q', the image of C,3) under the same translation? 12 13 A translation maps P(4,-3) onto P'(0, 0). Find the coordinates...
If a translation maps point (3, 2) to (4, 5); or T : (3, 2) (4, 5), indicate the image for (2, 4).
a. 1. Identify the image of point P under the following transformations. a translation along vector v b. a reflection across line 1 a counterclockwise rotation of 90° about point o d. A glide-reflection across / and along ū c. V E O u B C D A Р Identify the image of point P under the following transformations.
(1 point) Calculate: 4(1,3) =(
Define the linear transformation T:?3??4 by T(x )=Ax . Find a
vector x whose image under T is b
(1 pt) Let 4 5 2 -2 5 -3 2 and b-10 -7 2 1 -4 Define the linear transformation T : R3 ? R4 by T(x-Ax Find a vector x whose image under T is b. x= Is the vectorx unique? choose
(a) Find a Möbius transformation that maps 0 to, 1 to 2, and -1 to 4 (b) Let h(z)be the Möbius transformation and C: z-21 2 be the circle 2z-8 with centre 2 and radius 2. Determine the image of the interior of the circle C under h(z).
(a) Find a Möbius transformation that maps 0 to, 1 to 2, and -1 to 4 (b) Let h(z)be the Möbius transformation and C: z-21 2 be the circle 2z-8 with centre...
Pe (3) Show that the composite of two translations is again a translation (4) Show that the inverse of a translation is again a translation. (5) Suppose that f is an isometry which has no fixed points. Show that f can be written as a compo- sition Ro τ where T is a translation and R has at least one fixed point.
Pe (3) Show that the composite of two translations is again a translation (4) Show that the inverse...
please answer both
(12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0
(12(8 pts) Find parametric equations of the line through the point (2,...
Let T : P2 --> P4 be the transformation that maps a polynomial p(t) into the polynomial p(t) + t2p(t). (a) Find the image of p(t) = 2 - t + t2 (b) Show that T is a linear transformation. (c) Find the matrix for T relative to the bases {1, t, t2} and {1, t, t2, t3, t4}
Problem 2 [25 pts.] Let T: P2 → P4 be the transformation that maps a polynomial p(t) into the polynomial p(t) + tap(t). a. Find the image of p(t) 2 - t+t2. b. Show that T is a linear transformation. c. Find the matrix for T relative to the bases {1, t, ta} and {1, t, t2, t3, +4}.