Question

Type the correct answer in each box. Include a comma between the x- and y-coordinates. A triangle with the coordinates X(3, 2), Y(5, -1), and Z(-2, 3) is reflected across both the x- and y-axes. The coordinates after both reflections are X′( ), Y′( ), and Z′( ).

Answer 1

Answer: To reflect a point across the x-axis, you need to change the sign of its y-coordinate while keeping the x-coordinate the same. To reflect a point across the y-axis, you need to change the sign of its x-coordinate while keeping the y-coordinate the same.

In this case, we have the coordinates X(3, 2), Y(5, -1), and Z(-2, 3). Let's reflect each point across the x-axis first:

- The x-coordinate of X remains the same (3), but the y-coordinate becomes its opposite, so X' is (3, -2).

- The x-coordinate of Y remains the same (5), but the y-coordinate becomes its opposite, so Y' is (5, 1).

- The x-coordinate of Z remains the same (-2), but the y-coordinate becomes its opposite, so Z' is (-2, -3).

Now, let's reflect these new points across the y-axis:

- The y-coordinate of X' remains the same (-2), but the x-coordinate becomes its opposite, so X'' is (-3, -2).

- The y-coordinate of Y' remains the same (1), but the x-coordinate becomes its opposite, so Y'' is (-5, 1).

- The y-coordinate of Z' remains the same (-3), but the x-coordinate becomes its opposite, so Z'' is (2, -3).

Therefore, the coordinates after both reflections are X''(-3, -2), Y''(-5, 1), and Z''(2, -3).