Enter the ordered pair for the vertices for Rx-axis(QRST).

The graph with X-coordinate marks -4, -2, 0, 2, 4 and Y-coordinate marks -4, -2, -1, 0, 2, 4, 6. There is a polygon QRST with coordinates T at (-2, 3), Q at (1, 5), R at (3, -1) and S at (0, 0).

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erinna erinna · Answer 1 · 2020-11-13T02:25:02+01:00

Given:

The vertices of a polygon QRST are T(-2, 3), Q(1, 5), R(3, -1) and S(0, 0).

To find:

The vertices for [tex]R_{x-axis}(QRST)[/tex].

Solution:

The rule [tex]R_{x-axis}(QRST)[/tex] represents refection of polygon QRST across the x-axis.

If a figure is reflected across the x-axis, then

[tex](x,y)\to (x,-y)[/tex]

Using this rule, we get

[tex]T(-2,3)\to T'(-2,-3)[/tex]

[tex]Q(1,5)\to Q'(1,-5)[/tex]

[tex]R(3,-1)\to R'(3,1)[/tex]

[tex]S(0,0)\to S'(0,0)[/tex]

Therefore, the vertices for [tex]R_{x-axis}(QRST)[/tex] are T'(-2, -3), Q'(1, -5), R'(3, 1) and S'(0, 0).

MrRoyal MrRoyal · Answer 2 · 2021-11-11T13:54:56+01:00

Rx-axis means that the polygon QRST is reflected across the x-axis.

The ordered pair after Rx-axis is Q'(1,5), R'(3,1), S'(0,0) and T'(2,3)

The points are given as:

[tex]\mathbf{Q = (1,5)}[/tex]

[tex]\mathbf{R = (3,-1)}[/tex]

[tex]\mathbf{S = (0,0)}[/tex]

[tex]\mathbf{T = (-2,3)}[/tex]

The rule of reflection across the x-axis is:

[tex]\mathbf{(x,y) \to (x,-y)}[/tex]

So, we have:

[tex]\mathbf{Q' = (1,-5)}[/tex]

[tex]\mathbf{R' = (3,1)}[/tex]

[tex]\mathbf{S' = (0,0)}[/tex]

[tex]\mathbf{T' = (-2,-3)}[/tex]

Hence, the ordered pair after Rx-axis is Q'(1,5), R'(3,1), S'(0,0) and T'(2,3)