Find the value of t, if the distance between the points P(–3, –14) and Q(t, –5) is 9 units.

Answer Details

To find the value of t, we need to use the distance formula. The distance between two points in a coordinate plane can be found using the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the points are P(-3, -14) and Q(t, -5). We are given that the distance between these two points is 9 units. So we can set up the equation:
9 = sqrt((t - (-3))^2 + (-5 - (-14))^2)
Simplifying the equation, we get:
81 = (t + 3)^2 + 81
Now, let's solve for t.
Subtracting 81 from both sides:
0 = (t + 3)^2
Taking the square root of both sides:
0 = t + 3
Subtracting 3 from both sides:
t = -3
Therefore, the value of t is -3.
The correct answer is -3.