Point A (-3) B (7) marked on the coordinate line are equally distant from point C. find the cardinate of point C.

Point A (-3) B (7) marked on the coordinate line are equally distant from point C. find the cardinate of point C. Calculate the distance between points: 1) A and B. 2) A and C.

Let the points A (- 3) and B (7) be marked on the coordinate line, equally distant from the point C (x). Then the lengths of the segments AC and BC coincide: AC = BC. Knowing that AC = | x – (- 3) |, and BC = | 7 – x |, we compose the equation:

| x – (- 3) | = | 7 – x |, this equation is equivalent to two equations:

x – (- 3) = 7 – x or x – (- 3) = – (7 – x);

x + x = 7 + (- 3);

2 ∙ x = 4;

x = 2 – coordinate of point C;

the second equation has no solutions.

Answer: the coordinate of point C has a value of 2.

1). What is the distance between points A and B?

AB = | 7 – (- 3) | = 10 (unit segments).

2). What is the distance between points A and C?

AC = | 2 – (- 3) | = 5 (unit segments).

Answer: distance AB is 10 unit segments; the distance of the AC is 5 unit segments.