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The rule [tex]$T_{5,-0.5^{\circ}} R_{0,180^{\circ}}(x, y)$[/tex] is applied to [tex]$\Delta FGH$[/tex] to produce [tex]$\Delta F''G''H''$[/tex].

What are the coordinates of vertex [tex][tex]$F''$[/tex][/tex] of [tex]$\Delta F''G''H''$[/tex]?

A. [tex]$(4, -1.5)$[/tex]
B. [tex]$(4, -0.5)$[/tex]
C. [tex]$(-1.5, 4)$[/tex]
D. [tex]$(-0.5, 4)$[/tex]

Sagot :

GinnyAnswer
Let's solve this step-by-step using the given transformations. We're going to apply the transformations to the point [tex]\(F\)[/tex] with initial coordinates [tex]\((4, -1.5)\)[/tex].

First, we need to rotate the point [tex]\( (4, -1.5) \)[/tex] 180 degrees about the origin. A 180-degree rotation about the origin transforms a point [tex]\((x, y)\)[/tex] to [tex]\((-x, -y)\)[/tex].

- Original coordinates: [tex]\((4, -1.5)\)[/tex]
- Rotate 180 degrees: [tex]\((-4, 1.5)\)[/tex]

Next, we translate the resulting point [tex]\((-4, 1.5)\)[/tex] 5 units to the right and [tex]\(-0.5\)[/tex] units down.

- Translating 5 units to the right: [tex]\((-4 + 5, 1.5)\)[/tex] = [tex]\((1, 1.5)\)[/tex]
- Translating [tex]\(-0.5\)[/tex] units down: [tex]\((1, 1.5 - 0.5)\)[/tex] = [tex]\((1, 1.0)\)[/tex]

Therefore, the coordinates of vertex [tex]\( F^{\prime \prime} \)[/tex] of [tex]\( \Delta F^{\prime \prime} G^{\prime \prime} H^{\prime\prime} \)[/tex] are [tex]\((1, 1.0)\)[/tex].
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