A triangle on a coordinate plane has one verdict at (-7,-14) after a dilation with the origin as the center of dilation, the corresponding vertex of the dilated triangle is located at (-1, -2 ) which represents the dilation applied to the triangle
The dilation factor can be found by calculating the distance between the original vertex and the center of dilation, and the corresponding vertex and the center of dilation.
Original vertex: (-7, -14)
Center of dilation: (0, 0)
Distance between original vertex and center of dilation:
√((-7-0)^2 + (-14-0)^2) = √(49 + 196) = √245 ≈ 15.65
Corresponding vertex: (-1, -2)
Distance between corresponding vertex and center of dilation:
√((-1-0)^2 + (-2-0)^2) = √(1 + 4) = √5 ≈ 2.24
Dilation factor: √5 / √245 ≈ 2.24 / 15.65 ≈ 0.143
Therefore, the dilation factor is approximately 0.143.