Problema Solution
ABC is an isoceles right triangle in which AB has a slope of -1 and ABC=90. ABC is dilated by a scale factor of 1.8 with the origin as the center of dilation, resulting in the image A'B'C. What is the slope of B'C'?
Answer provided by our tutors
if the slope of AB is -1 this means that the angle between AB and x-axis is 135 degrees (tan 135 degrees = -1)
the angle ABC is 90 and the triangle is isosceles => the other two angles in the triangle are 45 degrees
if we draw the triangle we can see (and prove) that the slope of BC is 1 (the angle between x-axis and BC is 45 degrees and tan 45 = 1)
since angle measures are (invariant) under a dilation - they remain the same we can give the answer that the slope of B'C' is 1.
(draw the triangle and the dilatation to be able to see what really is going on)