Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To determine the type of triangle and the lengths of its sides, we first need to find the distances between the vertices.
1. Finding the length of [tex]\(AB\)[/tex]:
The formula for the distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
For points [tex]\(A (-2, 5)\)[/tex] and [tex]\(B (-4, -2)\)[/tex]:
[tex]\[ AB = \sqrt{((-4) - (-2))^2 + ((-2) - 5)^2} = \sqrt{(-2)^2 + (-7)^2} = \sqrt{4 + 49} = \sqrt{53} \approx 7.2801 \][/tex]
2. Finding the length of [tex]\(AC\)[/tex]:
For points [tex]\(A (-2, 5)\)[/tex] and [tex]\(C (3, -4)\)[/tex]:
[tex]\[ AC = \sqrt{((3) - (-2))^2 + ((-4) - 5)^2} = \sqrt{(5)^2 + (-9)^2} = \sqrt{25 + 81} = \sqrt{106} \approx 10.2956 \][/tex]
3. Finding the length of [tex]\(BC\)[/tex]:
For points [tex]\(B (-4, -2)\)[/tex] and [tex]\(C (3, -4)\)[/tex]:
[tex]\[ BC = \sqrt{((3) - (-4))^2 + ((-4) - (-2))^2} = \sqrt{(7)^2 + (-2)^2} = \sqrt{49 + 4} = \sqrt{53} \approx 7.2801 \][/tex]
Given these lengths:
- Length of [tex]\( AB \approx 7.2801 \)[/tex]
- Length of [tex]\( AC \approx 10.2956 \)[/tex]
- Length of [tex]\( BC \approx 7.2801 \)[/tex]
Next, we determine the type of triangle.
- If all three sides are equal, the triangle is equilateral.
- If exactly two sides are equal, the triangle is isosceles.
- If no sides are equal, the triangle is scalene.
Here, [tex]\( AB \approx 7.2801 \)[/tex] and [tex]\( BC \approx 7.2801 \)[/tex], while [tex]\( AC \approx 10.2956 \)[/tex]. Since two sides are approximately equal, the triangle is isosceles.
Therefore:
- The length of [tex]\(AB\)[/tex] is [tex]\( 7.2801 \)[/tex]
- The length of [tex]\(AC\)[/tex] is [tex]\(10.2956\)[/tex]
- The length of [tex]\(BC\)[/tex] is [tex]\( 7.2801 \)[/tex]
- The triangle is isosceles
1. Finding the length of [tex]\(AB\)[/tex]:
The formula for the distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
For points [tex]\(A (-2, 5)\)[/tex] and [tex]\(B (-4, -2)\)[/tex]:
[tex]\[ AB = \sqrt{((-4) - (-2))^2 + ((-2) - 5)^2} = \sqrt{(-2)^2 + (-7)^2} = \sqrt{4 + 49} = \sqrt{53} \approx 7.2801 \][/tex]
2. Finding the length of [tex]\(AC\)[/tex]:
For points [tex]\(A (-2, 5)\)[/tex] and [tex]\(C (3, -4)\)[/tex]:
[tex]\[ AC = \sqrt{((3) - (-2))^2 + ((-4) - 5)^2} = \sqrt{(5)^2 + (-9)^2} = \sqrt{25 + 81} = \sqrt{106} \approx 10.2956 \][/tex]
3. Finding the length of [tex]\(BC\)[/tex]:
For points [tex]\(B (-4, -2)\)[/tex] and [tex]\(C (3, -4)\)[/tex]:
[tex]\[ BC = \sqrt{((3) - (-4))^2 + ((-4) - (-2))^2} = \sqrt{(7)^2 + (-2)^2} = \sqrt{49 + 4} = \sqrt{53} \approx 7.2801 \][/tex]
Given these lengths:
- Length of [tex]\( AB \approx 7.2801 \)[/tex]
- Length of [tex]\( AC \approx 10.2956 \)[/tex]
- Length of [tex]\( BC \approx 7.2801 \)[/tex]
Next, we determine the type of triangle.
- If all three sides are equal, the triangle is equilateral.
- If exactly two sides are equal, the triangle is isosceles.
- If no sides are equal, the triangle is scalene.
Here, [tex]\( AB \approx 7.2801 \)[/tex] and [tex]\( BC \approx 7.2801 \)[/tex], while [tex]\( AC \approx 10.2956 \)[/tex]. Since two sides are approximately equal, the triangle is isosceles.
Therefore:
- The length of [tex]\(AB\)[/tex] is [tex]\( 7.2801 \)[/tex]
- The length of [tex]\(AC\)[/tex] is [tex]\(10.2956\)[/tex]
- The length of [tex]\(BC\)[/tex] is [tex]\( 7.2801 \)[/tex]
- The triangle is isosceles
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.