Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Given that the midpoint of the line segment is [tex]\((11, -5)\)[/tex] and one endpoint of the line segment is [tex]\((-4, -8)\)[/tex], we are to find the coordinates of the other endpoint.
We use the midpoint formula, which is:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
where [tex]\( M \)[/tex] is the midpoint, and [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are the coordinates of the two endpoints.
For our problem:
- The midpoint [tex]\(M\)[/tex] is [tex]\((11, -5)\)[/tex]
- One endpoint [tex]\((x_1, y_1)\)[/tex] is [tex]\((-4, -8)\)[/tex]
- We need to find the coordinates [tex]\((x_2, y_2)\)[/tex] of the other endpoint.
Let's set up the equations from the midpoint formula:
[tex]\[ 11 = \frac{-4 + x_2}{2} \][/tex]
[tex]\[ -5 = \frac{-8 + y_2}{2} \][/tex]
We solve these equations step-by-step.
Step 1: Solve for [tex]\(x_2\)[/tex]
[tex]\[ 11 = \frac{-4 + x_2}{2} \][/tex]
Multiply both sides by 2 to clear the fraction:
[tex]\[ 22 = -4 + x_2 \][/tex]
Add 4 to both sides to solve for [tex]\(x_2\)[/tex]:
[tex]\[ x_2 = 22 + 4 \][/tex]
[tex]\[ x_2 = 26 \][/tex]
Step 2: Solve for [tex]\(y_2\)[/tex]
[tex]\[ -5 = \frac{-8 + y_2}{2} \][/tex]
Multiply both sides by 2 to clear the fraction:
[tex]\[ -10 = -8 + y_2 \][/tex]
Add 8 to both sides to solve for [tex]\(y_2\)[/tex]:
[tex]\[ y_2 = -10 + 8 \][/tex]
[tex]\[ y_2 = -2 \][/tex]
Thus, the coordinates of the other endpoint are [tex]\((26, -2)\)[/tex].
The correct answer is [tex]\((26, -2)\)[/tex].
We use the midpoint formula, which is:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
where [tex]\( M \)[/tex] is the midpoint, and [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are the coordinates of the two endpoints.
For our problem:
- The midpoint [tex]\(M\)[/tex] is [tex]\((11, -5)\)[/tex]
- One endpoint [tex]\((x_1, y_1)\)[/tex] is [tex]\((-4, -8)\)[/tex]
- We need to find the coordinates [tex]\((x_2, y_2)\)[/tex] of the other endpoint.
Let's set up the equations from the midpoint formula:
[tex]\[ 11 = \frac{-4 + x_2}{2} \][/tex]
[tex]\[ -5 = \frac{-8 + y_2}{2} \][/tex]
We solve these equations step-by-step.
Step 1: Solve for [tex]\(x_2\)[/tex]
[tex]\[ 11 = \frac{-4 + x_2}{2} \][/tex]
Multiply both sides by 2 to clear the fraction:
[tex]\[ 22 = -4 + x_2 \][/tex]
Add 4 to both sides to solve for [tex]\(x_2\)[/tex]:
[tex]\[ x_2 = 22 + 4 \][/tex]
[tex]\[ x_2 = 26 \][/tex]
Step 2: Solve for [tex]\(y_2\)[/tex]
[tex]\[ -5 = \frac{-8 + y_2}{2} \][/tex]
Multiply both sides by 2 to clear the fraction:
[tex]\[ -10 = -8 + y_2 \][/tex]
Add 8 to both sides to solve for [tex]\(y_2\)[/tex]:
[tex]\[ y_2 = -10 + 8 \][/tex]
[tex]\[ y_2 = -2 \][/tex]
Thus, the coordinates of the other endpoint are [tex]\((26, -2)\)[/tex].
The correct answer is [tex]\((26, -2)\)[/tex].
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.