Question

Points A and B are on different sides of line l. The distance between point A and line l is 10 in. The distance between point B and line l is 4 in. What is the distance between midpoint O of segment AB and line l?

a) 7 in
b) 6 in
c) 5 in
d) 4 in

Answer 1

The distance between midpoint O of segment AB and line l is 7 inches, as it is the average of the distances from points A and B to line l, which are 10 inches and 4 inches respectively.

Step-by-step explanation:

The question asks us to find the distance between the midpoint O of segment AB and line l, given that the distance from point A to line l is 10 inches and the distance from point B to line l is 4 inches. To find this, we know that points A and B are on opposite sides of line l, and the perpendicular distances from a point to a line are consistent along the entire length of the line.

Therefore, the distance from point A to line l plus the distance from point B to line l is the sum of the two distances, which is 10 inches + 4 inches = 14 inches. The midpoint O of segment AB is exactly halfway between the two distances, so the distance from O to line l would be half of the sum of the two distances.

So, the distance from midpoint O to line l is (10 inches + 4 inches) / 2 = 14 inches / 2 = 7 inches. Therefore, the correct answer is (a) 7 inches.