Lakie is given two side lengths and the measure of the angle between them. how many unique triangles can she form given this information?

She can form only one such triangle. The given angle 'fixes' the shape of the triangle. Once the angle is given, the third side is also fixed.

So we have the first 2 sides, say a and b, and the third side c, fixed by fixing the angle between a and b. By Side Side Side congruence postulate, any triangle with sides a, b, c will be the exact same triangle as the one we constructed.

a translation of 2 units to the left and 7 units up

Step-by-step explanation:

Translation of points (x,y)

At point x, the function can be translated to the left or to the right.

(x-a) is the translation of the point a units to the left, and (x+a) is the translation of the point a units to the right.

At point x, the function can be translated up or down. y+a represents a shift of a units up, and y-a represents a shift of a units down.

(x, y) = (x - 2, y + 7)

x - 2: 2 units to the left.

y + 7: 7 units up

So the fouth option is correct.