Question

A trlangle wlth vertices at A0, 0), B0, 4), and C(6, 0) Is dilated to yleld a trlangle with vertices at A [0, 0), B(O, 10), and C(15, 0). The orlgin Is the center of dllation. What Is the scale factor of the dilatlon? A. 1.5 B. 2 C. 2.5 D. 3​

Answer 1

The scale factor of the dilation is determined by comparing the dimensions of the original and dilated triangles. Given the provided choices, the correct scale factor is 2.5, which corresponds to option C.

Step-by-step explanation:

The question is asking for the scale factor of a dilation transformation of a triangle with vertices. To find the scale factor, we compare the corresponding sides of the original and dilated triangles. For example, in the original triangle, the distance between points B (0,4) and C (6,0) is calculated using the distance formula or by simply observing that it is a right triangle with a vertical side of 4 units and a horizontal side of 6 units, giving us a distance of 8 units along the hypotenuse by applying the Pythagorean theorem. Similarly, the dilated triangle's side BC is from B (0,10) to C (15,0), yielding a new hypotenuse length by the same logic of 25 units. The scale factor is then the ratio of the dilated triangle's side to the original triangle's side, which in this case is 25/8 or 3.125, which is not an option in the given choices. However, if we compare the dilation of just the vertical side of the triangle at B or the horizontal side at C, the scale factor is 10/4 = 2.5 or 15/6 = 2.5 respectively, which matches option C.