Question

Given A(-1,10) and B(x,2), find the values of x if AB=10. There are two answers!

A) x = -9 and x = 7
B) x = 9 and x = -7
C) x = 11 and x = -5
D) x = -11 and x = 5

Answer 1

To find the values of x for points A(-1,10) and B(x,2) with a distance AB of 10, we use the distance formula and solve for x, yielding two solutions: x = -7 and x = 5.

Step-by-step explanation:

The student asked for the values of x if the distance between points A(-1,10) and B(x,2) is 10 units. To solve this, we can use the distance formula, which is derived from the Pythagorean theorem: AB = √[(x2 - x1)2 + (y2 - y1)2]. In this context, (x1, y1) is point A, and (x2, y2) is point B.

We set the formula equal to 10: 10 = √[(x - (-1))2 + (2 - 10)2], then simplify and solve for x. Squaring both sides gives us 100 = (x + 1)2 + 64. This further simplifies to (x + 1)2 = 36, leading to x + 1 = ±6. Therefore, the two possible values for x are -1 - 6 and -1 + 6, which gives us x = -7 and x = 5.