12. decide whether each statement is always true, sometimes true, or never true. a. when corresponding points of an original figure and its reflection are connected, the resulting segments are all perpendicular to the line of reflection. b. when a point is reflected over a horizontal line, the y-coordinate of the point stays the same. answer both questions and explain

A. Always True

B. Never True

Step-by-step explanation:

A. We have,

The corresponding points of an original figure and its reflection are located at the same distance from the axis of reflection.

So, the axis of reflection will bisect the line joining the corresponding points perpendicularly.

Thus, the line segments are always perpendicular to the axis of reflection.

B. We know that,

The co-ordinates (x,y) lying in the first quadrant, after refection over x-axis (or the horizontal line) will become (x,-y).

So, the y-coordinate changes its sign after reflection over x-axis.

Thus, y-coordinate is never same after reflection over horizontal line.

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation:

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.