The vertices of quadrilateral mnpq are m(-3,-2), n(-1,4), p(2,4), q(4,-2). translate quadrilateral mnpq using the rule (x, y)-> (x+3, y+4)

Therefore, if the vertices of quadrilateral MNPQ given as M(-3,-2), N(-1,4), P(2,4), Q(4,-2) are translated using the rule (x,y)->(x+3, y+4), then the vertices of the quadrilateral M'N'P'Q' are M'(0,  2), N'(2,  8), P'(5,  8), and Q'(7,  2)

The vertices of the quadrilateral are:

M(-3,-2), N(-1,4), P(2,4), Q(4,-2)

The rule of translation is:

(x,y)->(x+3, y+4)

Following the rule of translation above, add 3 to the x-coordinate and 4 to the y-coordinate

The vertices of the quadrilateral M'N'P'Q' are:

M'(-3+3,  -2+4)  =  M'(0,  2)

N'(-1+3,  4 + 4)   =  N'(2,  8)

P'(2+3,  4 + 4)   =  P'(5,  8)

Q'(4+3,  -2+4)   =  Q'(7,  2)

Therefore, if the vertices of quadrilateral MNPQ given as M(-3,-2), N(-1,4), P(2,4), Q(4,-2) are translated using the rule (x,y)->(x+3, y+4), then the vertices of the quadrilateral M'N'P'Q' are M'(0,  2), N'(2,  8), P'(5,  8), and Q'(7,  2)

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Here's what I get.

Step-by-step explanation:

The rule is (x, y) ⟶ (x + 3, y + 4).

That means you must move each point three units to the right and four units up.  Thus,

M(-3, -2) ⟶ M'(0, 2)

N(-1, 4)  ⟶ N'(2, 8)

P(2, 4)    ⟶ P'(5, 8)

Q(4, -2)  ⟶ Q'(7, 2)  

Your quadrilateral is a trapezoid. Both MNPQ and its image M'N'P'Q' are shown in the Figure below.