Rectangle abcd has vertices a(–6, –2), b(–3, –2), c(–3. –6), and d(–6, –6). the rectangle is translated so that the coordinates of the image are a’(–10, 1), b’(–7,1), c’(–7, –3), and d’(–10, –3). which rule was used to translate the image?

 The required rule of translation is  (x, y) ⇒  (x-4, y+3).

Step-by-step explanation:  Given that rectangle ABCD has vertices A(–6, –2), B(–3, –2), C(–3. –6), and D(–6, –6).

The rectangle ABCD is translated so that the coordinates of the image are A’(–10, 1), B’(–7,1), C’(–7, –3), and D’(–10, –3).

We are to find the rule that is used to translate the image.

We know that

if a point (x, y) is translated h units to the left and k units up, then the co-ordinates of the translated point will be

(x - h, y + k).

From the co-ordinates of the vertices of rectangle ABCD and its image A'B'C'D', we see the following translation :

A(-6, -2)  ⇒   A'(-6-4, -2+3)  = A'(-10, 1),

B(-3, -2)  ⇒   B'(-3-4, -2+3)  = A'(-7, 1),

C(-3, -6)  ⇒   C'(-3-4, -6+3)  = C'(-7, -3),

D(-6, -6)  ⇒   D'(-6-4, -6+3)  = D'(-10, -3).

Thus, the required rule of translation is  (x, y) ⇒  (x-4, y+3).

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116