Answer to Question #241586 in Geometry for Lili

Question #241586

In the coordinate plane the point x (-4,4) is translated to the point x (0,-1). Under the same translation the points Y (-2,0) and Z (-1,6) are translated to Y and Z, respectively. What are the coordinates of Y and Z?

a response urges me please


1
Expert's answer
2021-09-26T15:54:47-0400

Find the translation vector

Let the translation vector be "\\begin{pmatrix}\n a \\\\\n b\n\\end{pmatrix}"

"\\begin{pmatrix}\n a\\\\\n b \n\\end{pmatrix}+\\begin{pmatrix}\n -4 \\\\\n 4\n\\end{pmatrix}=\\begin{pmatrix}\n 0\\\\\n -1\n\\end{pmatrix}"

"a-4=0, a=4"

"b+4=-1, b=-5"

The translation vector is "\\begin{pmatrix}\n 0 \\\\\n -5\n\\end{pmatrix}"

find coordinates of Y

"\\begin{pmatrix}\n 0 \\\\\n -5\n\\end{pmatrix}+\\begin{pmatrix}\n -2 \\\\\n 0\n\\end{pmatrix}=\\begin{pmatrix}\n -2 \\\\\n -5\n\\end{pmatrix}"

coordinates of Y is (-2, -5)

Find the coordinates of Z

"\\begin{pmatrix}\n 0 \\\\\n -5\n\\end{pmatrix}+\\begin{pmatrix}\n -1\\\\\n 6\n\\end{pmatrix}=\\begin{pmatrix}\n -1 \\\\\n 1\n\\end{pmatrix}"

coordinates of Z is (-1, 1)


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