Question

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)

Answer 1

Answer:

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

$(x,y)\rightarrow (x+a,y+b)$

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.

$(x,y)\rightarrow (x+2,y+3)$

Therefore, the correct option is d.

Answer 2

Under the transformation of Triangle PQR by (d) (x, y) --> (x + 2, y + 3), the distance and angle measure are preserved

How to determine the transformation?

For the distance and angle measure to be preserve, then the transformation must be a rigid transformation

The rigid transformations are:

• Reflection
• Translation
• Rotation

From the list of options, (d) (x, y) --> (x + 2, y + 3) is a translation of the triangle

Hence, the transformation of Triangle PQR by (d) (x, y) --> (x + 2, y + 3), preserves the distance and angle measure

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