Polygon pqrst shown below is dilated with a scale factor of 3 l, keeping the origin as the center of dilation:
which statement about polygon pqrst and its image after dilation, polygon p’q’r’s’t, is correct?
the length of diagonal ps and diagonal p’s’ are in the ratio 1: 3
the lengths of side pt and side r’q’ are in ratio 1: 3
the length of side pt is equal to the length of side p’t’
the measures of angle s and angle s’ are in the ratio 1: 3

Lian is deciding which of two gyms to join. each gym charges a monthly rate plus a one-time membership fee. lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. in her work, she substituted an expression for one variable and solved for the other. this resulted in the equation 75 = 75. what can lian conclude? one gym charges $75 per month. each gym charges $75 per month both gyms charge the same monthly rate and the same membership fee. both gyms charge the same monthly rate, but not the same membership fee.