Question

Triangle abc with vertices a (−1, 2), b (−1, −2) , and c (−4, −2) is enlarged by doubling the side lengths to form triangle xyz. what is the length, in units, of side xy

Answer 1

The length of side XY of the enlarged triangle is 8 units, as it is double the length of side AB in the original triangle, which is 4 units.

Step-by-step explanation:

To determine the length of side XY in an enlarged triangle with vertices A (-1, 2), B (-1, -2), and C (-4, -2), first identify the original length of AB in triangle ABC. Since A and B have the same x-coordinate, the length of AB is simply the difference in their y-coordinates, which is 2 - (-2) = 4 units. After enlarging the triangle by doubling the side lengths, the new length of side XY would be double that of AB, thus 4 units x 2 = 8 units.

To formally validate this, you can use the distance formula: \(d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\), but in this case, the calculation simplifies because the x-coordinates are identical.