Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To find the length of [tex]\(\overline{DE}\)[/tex], given that the triangle was dilated by a scale factor of 2 and [tex]\(\overline{FD}\)[/tex] measures 6 units, you need to apply the property of dilation.
When a geometric figure is dilated by a scale factor, all lengths in the figure are multiplied by that scale factor.
Here’s a step-by-step explanation:
1. The original length of [tex]\(\overline{FD}\)[/tex] is given as 6 units.
2. The dilation process increases all lengths in the figure by the scale factor.
In this problem, the scale factor is 2.
3. To find the new length of [tex]\(\overline{DE}\)[/tex], multiply the original length [tex]\(\overline{FD}\)[/tex] by the scale factor:
[tex]\[ \overline{DE} = \overline{FD} \times \text{scale factor} \][/tex]
4. Substituting the given values:
[tex]\[ \overline{DE} = 6 \, \text{units} \times 2 \][/tex]
5. This calculation gives:
[tex]\[ \overline{DE} = 12 \, \text{units} \][/tex]
Therefore, the length of [tex]\(\overline{DE}\)[/tex] is [tex]\(12\)[/tex] units. The correct answer is:
[tex]\[ \boxed{\overline{DE}=12} \][/tex]
When a geometric figure is dilated by a scale factor, all lengths in the figure are multiplied by that scale factor.
Here’s a step-by-step explanation:
1. The original length of [tex]\(\overline{FD}\)[/tex] is given as 6 units.
2. The dilation process increases all lengths in the figure by the scale factor.
In this problem, the scale factor is 2.
3. To find the new length of [tex]\(\overline{DE}\)[/tex], multiply the original length [tex]\(\overline{FD}\)[/tex] by the scale factor:
[tex]\[ \overline{DE} = \overline{FD} \times \text{scale factor} \][/tex]
4. Substituting the given values:
[tex]\[ \overline{DE} = 6 \, \text{units} \times 2 \][/tex]
5. This calculation gives:
[tex]\[ \overline{DE} = 12 \, \text{units} \][/tex]
Therefore, the length of [tex]\(\overline{DE}\)[/tex] is [tex]\(12\)[/tex] units. The correct answer is:
[tex]\[ \boxed{\overline{DE}=12} \][/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.