Find the value of t if the distance between the... - JAMB Mathematics 2023 Question
Find the value of t, if the distance between the points P(–3, –14) and Q(t, –5) is 9 units.
A
3
B
2
C
- 3
D
- 2
correct option: c
The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a plane is given by the distance formula:
\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
In this case, the coordinates of points P and Q are \((-3, -14)\) and \((t, -5)\) respectively.
The distance between P and Q is given as 9 units. Substituting the coordinates into the formula:
\[9 = \sqrt{(t - (-3))^2 + ((-5) - (-14))^2}\]
\[9 = \sqrt{(t + 3)^2 + 9^2}\]
\[81 = (t + 3)^2 + 81\]
Now, let's solve for \(t\):
\[0 = (t + 3)^2\]
The only solution to this quadratic equation is \(t = -3\).
Therefore, the correct answer is -3
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