Question

The vertices of quadrilateral MNPQ are M(−3,−2),N(−1,4),P(2,4), and Q(4,−2). Translate quadrilateral MNPQ using the vector ⟨3,−4⟩.

Answer 1

M'(0,-6),N'(2,0),P'(5,0) and Q'(7,-6)

Explanation:

We are given that the vertices of quadrilateral MNPQ are M(-3,-2),N(-1,4),P(2,4) and Q(4,-2).

We have to translate the quadrilateral MNPQ using vector <3,-4>

The translate the coordinates of vertices (x,y) using the vector <a,b> is given by the rule

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

Using the rule

The new coordinates of M

`(-3,-2)\rightarrow (-3+3,-4-2)`

`(-3,-2)\rightarrow (0,-6)`

The new coordinates of N

`(-1,4)\rightarrow (2,0)`

The new coordinates of P

`(2,4)\rightarrow (5,0)`

The new coordinates of Q

`(4,-2)\rightarrow (7,-6)`

Hence, after translation the new vertices of quadrilateral are

M'(0,-6),N'(2,0),P'(5,0) and Q'(7,-6)