Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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].
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.