Question

Garrus, Lily, and Lincoln all live in the same neighborhood. Calculate the distances between their houses and classify the triangle.

a) Equilateral
b) Isosceles
c) Scalene
d) none of the above

Answer 1

To calculate the distances between their houses and classify the triangle, you can use the distance formula derived from the Pythagorean theorem. After finding the distances, you can determine if the triangle is equilateral, isosceles, scalene, or none of the above.

Step-by-step explanation:

To calculate the distances between their houses, we can use the distance formula, which is derived from the Pythagorean theorem. Let's assume Garrus, Lily, and Lincoln live at points A, B, and C, respectively. The distance between A and B is AB, between B and C is BC, and between C and A is CA.

1. Calculate the distance AB using the coordinates of points A and B: AB = sqrt((x2 - x1)^2 + (y2 - y1)^2).
2. Calculate the distance BC using the coordinates of points B and C: BC = sqrt((x3 - x2)^2 + (y3 - y2)^2).
3. Calculate the distance CA using the coordinates of points C and A: CA = sqrt((x1 - x3)^2 + (y1 - y3)^2).

After finding the distances, we can classify the triangle based on the lengths of its sides:

• If AB = BC = CA, then the triangle is equilateral.
• If two sides of the triangle are equal, but the third side is different, then the triangle is isosceles.
• If all three sides of the triangle are different, then the triangle is scalene.
• If none of the conditions are met, then the triangle does not fall into any of the mentioned categories (none of the above).