In #1-2, find the value of each variable.
1) Translation \((x, y)\rightarrow(x + 1, y + 3)\)
a) \(A(-12, 5c), A'(1 - 3d, 13)\)
b) \(B(3e + 2, 12), B'(-6, 3f)\)
2) Translation \((x, y)\rightarrow(x - 2, y - 4)\)
a) \(A(-g, 2), A'(-3, 3h + 1)\)
b) \(B(j + 4, j), B'(0, 4 - k)\)
3) The vertices of a rectangle are \(M(2, -3), A(2, 4), T(5, 4), H(5, -3)\).
a) Translate \(MATH\) three units left and two units down. Find the areas of \(MATH\) and \(M'A'T'H'\).
b) Compare the areas. Make a conjecture about the areas of a pre-image and its image after a translation.
4) The vertices of \(\triangle YES\) are \(Y(2, 2), E(4, 2), S(3, 4)\). Find the image of \(\triangle YES\) after the transformation \((x, y)\rightarrow(x + y, y)\). Is the transformation an isometry? Explain your reasoning. Are the areas of \(\triangle YES\) and \(\triangle Y'E'S'\) the same?
5) Given \(f(x) = -\Large\frac{7}{3}\normalsize x - 5\). What would the image of the function be with a translation of six units down and five units right?
6) Given \(g(x) = -\Large\frac{7}{3}\normalsize(x - 9)\). What would the image of the function be with \((x, y)\rightarrow(x - 4, y + 0.5)\)?
7) Given a translation of \(\big\langle-2, -7\big\rangle\). What is the preimage of the function \(h(x) = -\Large\frac{7}{3}\normalsize x + 4\)?
8) Use the graph below to answer the questions.
a) What is the equation for function \(a\), the parent function?
b) What is the translation vector from the parent function and the equation for function \(b\)?
c) What is the translation vector from the parent function and the equation for function \(c\)?
d) What is the translation vector from the parent function and the equation for function \(d\)?
1) Translation \((x, y)\rightarrow(x + 1, y + 3)\)
a) \(A(-12, 5c), A'(1 - 3d, 13)\)
b) \(B(3e + 2, 12), B'(-6, 3f)\)
2) Translation \((x, y)\rightarrow(x - 2, y - 4)\)
a) \(A(-g, 2), A'(-3, 3h + 1)\)
b) \(B(j + 4, j), B'(0, 4 - k)\)
3) The vertices of a rectangle are \(M(2, -3), A(2, 4), T(5, 4), H(5, -3)\).
a) Translate \(MATH\) three units left and two units down. Find the areas of \(MATH\) and \(M'A'T'H'\).
b) Compare the areas. Make a conjecture about the areas of a pre-image and its image after a translation.
4) The vertices of \(\triangle YES\) are \(Y(2, 2), E(4, 2), S(3, 4)\). Find the image of \(\triangle YES\) after the transformation \((x, y)\rightarrow(x + y, y)\). Is the transformation an isometry? Explain your reasoning. Are the areas of \(\triangle YES\) and \(\triangle Y'E'S'\) the same?
5) Given \(f(x) = -\Large\frac{7}{3}\normalsize x - 5\). What would the image of the function be with a translation of six units down and five units right?
6) Given \(g(x) = -\Large\frac{7}{3}\normalsize(x - 9)\). What would the image of the function be with \((x, y)\rightarrow(x - 4, y + 0.5)\)?
7) Given a translation of \(\big\langle-2, -7\big\rangle\). What is the preimage of the function \(h(x) = -\Large\frac{7}{3}\normalsize x + 4\)?
8) Use the graph below to answer the questions.
a) What is the equation for function \(a\), the parent function?
b) What is the translation vector from the parent function and the equation for function \(b\)?
c) What is the translation vector from the parent function and the equation for function \(c\)?
d) What is the translation vector from the parent function and the equation for function \(d\)?