The distance between P(x, 7) and Q(6, 19) is 13 units. Find the values of x.
Question 1 Report
The distance between P(x, 7) and Q(6, 19) is 13 units. Find the values of x.
Answer Details
To find the value of x, we can use the distance formula which states that the distance between two points P(x1, y1) and Q(x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, we are given the distance between P(x, 7) and Q(6, 19) as 13 units. Therefore, we can write:
13 = sqrt((6 - x)^2 + (19 - 7)^2)
Simplifying this equation, we get:
169 = (6 - x)^2 + 144
25 = (6 - x)^2
Taking the square root of both sides, we get:
5 = 6 - x or 5 = x - 6
Solving for x in each case, we get:
x = 1 or x = 11
Therefore, the possible values of x are 1 or 11.
Note that we can also check that the distance between P(1, 7) and Q(6, 19) and between P(11, 7) and Q(6, 19) is indeed 13 units.
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