Quadrilateral klmn has vertices k(-2,-2), l(1,1), m(0,4), and n(-3,5). it is first translated by (x + 2,y - 1) and then translated by (x - 3,y + 4). when a figure is translated twice, a double prime symbol is used. find the coordinates of k" l" m" n" after both translations.

Quadrilateral KLMN has vertices K(-2,-2), L(1,1), M(0,4), and N(-3,5)
 It is first translated by (x + 2,y - 1)
 then
 K(-2,-2) ---> K'(-2 + 2,-2 - 1) = (0,-3)
 L(1,1), ---> L'(1 + 2,1 - 1) = (3,0)
 M(0,4), ---> M' (0 + 2,4 - 1) = (2,3)
 and
 N(-3,5) ---> N' (-3 + 2,5 - 1) = (-1,4)
 and then translated by (x - 3,y + 4)
 K'(0,-3) ---> K''(0 - 3,-3 + 4) = (-3,1)
 L'(3,0) ---> L''(3 - 3,0 + 4)= (0,4)
 M'(2,3)  ---> M'' (2 - 3, 3 + 4)= (-1,7)
 and 
 N'(-1,4) ---> N'' (-1 - 3,4 + 4) = (-4,8)
 the coordinates of K" L" M" N" after both translations are
 K''= (-3,1)
 L''= (0,4)
 M''= (-1,7)
 and 
 N'' = (-4,8)

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.