Question

properties of transformations
quiz complete
a square with side lengths of 4 units is translated on the coordinate plane. one vertex of the image is at (2, 1).
which ordered pair could represent another vertex of the image?
(0, -1)
(2, 6)
(4, 0)
(6, 1)
mark this and return save and exit next submit

Explanation:

Step1: Analyze the properties of a square

In a square, adjacent vertices have a distance equal to the side - length. The side - length of the square is \(4\) units.

Step2: Calculate the distance between the given vertex \((2,1)\) and each option

• For the point \((0, - 1)\):

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1 = 2,y_1 = 1,x_2=0,y_2=-1\). Then \(d=\sqrt{(0 - 2)^2+(-1 - 1)^2}=\sqrt{4 + 4}=\sqrt{8}
eq4\)

• For the point \((2,6)\):

Here \(x_1 = 2,y_1 = 1,x_2 = 2,y_2 = 6\). Then \(d=\sqrt{(2 - 2)^2+(6 - 1)^2}=\sqrt{0 + 25}=5
eq4\)

• For the point \((4,0)\):

Here \(x_1 = 2,y_1 = 1,x_2 = 4,y_2 = 0\). Then \(d=\sqrt{(4 - 2)^2+(0 - 1)^2}=\sqrt{4+1}=\sqrt{5}
eq4\)

• For the point \((6,1)\):

Here \(x_1 = 2,y_1 = 1,x_2 = 6,y_2 = 1\). Then \(d=\sqrt{(6 - 2)^2+(1 - 1)^2}=\sqrt{16+0}=4\)

Answer:

\((6,1)\)