Question
If p is the point (a,6) and its distance to the point (-3,2) is 5, determine the value of A
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Answer to a math question If p is the point (a,6) and its distance to the point (-3,2) is 5, determine the value of A
Corbin
4.6107 Answers
1. Start with the distance formula:
\sqrt{(a + 3)^2 + (6 - 2)^2} = 5
2. Simplify inside the square root:
\sqrt{(a + 3)^2 + 4^2} = 5
3. Simplify:
\sqrt{(a + 3)^2 + 16} = 5
4. Square both sides to eliminate the square root:
(a + 3)^2 + 16 = 25
5. Subtract 16 from both sides to isolate the square term:
(a + 3)^2 = 9
6. Solve for ( a ) by taking the square root of both sides:
a + 3 = \pm 3
7. This gives two potential values for ( a ):
a + 3 = 3 \quad \Rightarrow \quad a = 0
a + 3 = -3 \quad \Rightarrow \quad a = -6
8. Therefore, the solutions are:
a = 0 \text{ or } a = -6
2. Simplify inside the square root:
3. Simplify:
4. Square both sides to eliminate the square root:
5. Subtract 16 from both sides to isolate the square term:
6. Solve for ( a ) by taking the square root of both sides:
7. This gives two potential values for ( a ):
8. Therefore, the solutions are:
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