The vertices of triangle pqr have coordinates p(2, 3), q(3, 8), and r(7, 3). under which transformation of triangle pqr are distance and angle measure preserved?
a) (x, y) --> (2x, 3y)
b) (x, y) --> (x + 2, 3y)
c) (x, y) --> (2x, y + 3)
d) (x, y) --> (x + 2, y + 3)

Option d.

Step-by-step explanation:

It is given that vertices of triangle PQR have coordinates P(2, 3), Q(3, 8), and R(7, 3).

We need to find the transformation of Triangle PQR, so that distance and angle measure preserved.

We know that translation is a rigid transformation if the rule of translation is

where, a represents the horizontal shift and b represent the vertical shift.

To for a congruent triangle the coefficients of x and y must be 1.

Only in option d the coefficients of x and y are 1.

Therefore, the correct option is d.