Question 1: Parallel lines are two lines in a plane that are always the same distance apart and never intersect. The locus of points equidistant from both lines forms a set of lines parallel to them. The key formula involves understanding that the distance between parallel lines remains constant.

Answer: See full answer key

Question 1: Calculate the distance between two parallel kitchen counters if they are 2 meters apart and run alongside each other.

Answer: 2 meters

Question 2: Construct two parallel shelves in a pantry that are 30 cm apart. If one shelf starts at position x=10 cm, find the position of the second shelf.

Answer: 40 cm

Question 3: Plot the graph of y = 2x and draw a line parallel to it that is 4 units away.

Answer: Line y=2x+4 or y=2x-4

Question 1: A chef designs two parallel conveyor belts in a bakery that are 1.5 meters apart. If the bakery layout changes and the belts are moved 20 cm further apart, what is the new distance between them?

Answer: 1.7 meters

Question 2: In a kitchen, two parallel walls are 4 meters long. A cabinet is to be placed 1 meter away from one wall. How far is the cabinet from the other wall if it is exactly in the middle of the two walls?

Answer: 2 meters

Question 3: Explain how the locus of points equidistant from two parallel lines forms a set of lines parallel to them, using a kitchen countertop as an example.

Answer: The set of points that are equally distant from both counters forms lines parallel to them, representing the locus. For example, if the counters are 1 meter apart, the locus is a line exactly midway, also parallel, at 0.5 meters from each.

Question 1: A chef wants to install two parallel spice racks 15 cm apart on opposite walls of a narrow pantry. If the racks are 2 meters high, what is the shortest distance the chef must measure between the racks at their top and bottom?

Answer: 15 cm

Question 2: In a bakery, two conveyor belts run parallel, 1.2 meters apart. If the layout is changed to make one belt 20 cm further from the wall, what is the new distance between the belts?

Answer: 1.4 meters

Question 3: A recipe calls for a strip of dough to be cut in a straight line 3 cm away from the edge of the work surface. The work surface has two parallel edges 60 cm apart. How far is the cut line from the opposite edge if the line is exactly midway?

Answer: 30 cm

Question 1: Design a layout for two parallel counters running through a kitchen, making sure they are 0.75 meters apart. If the counters are 4 meters long, find the coordinates of their start points if one starts at (2,3).

Answer: Start points at (2,3) and (2,3+0.75)

Question 2: Given two parallel lines representing shelves, each 50 cm long, separated by 20 cm, find the total length of the locus of points exactly 10 cm from both shelves, assuming the shelves are aligned along the x-axis.

Answer: The locus forms lines parallel to shelves; total length depends on the segment, so answer: 50 cm each side, total 100 cm.

Question 1: A student states: 'Two parallel lines are 5 meters apart, and the locus of points equidistant from both is a line that is 5 meters away from each line.' Is this statement correct? Explain your answer.

Answer: Incorrect; the locus is exactly midway, 2.5 meters from each line.

Question 2: A mistake was made when drawing two parallel lines 3 cm apart, claiming the locus of points equidistant from both is a single line. Why is this wrong, and what should the locus look like?

Answer: The locus is actually two lines parallel to the original lines, each 1.5 cm from the original lines, forming a band.