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If the distance between the points (p, – 5) and (2, 7) is 13 units, then the value of ‘p’ is
- a)– 3, 7
- b)3, – 7
- c)– 3, – 7
- d)3, 7
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the distance between the points (p, – 5) and (2, 7) is 13 uni...
Explanation:
Let point A be (p,−5) and point B (2, 7) and distance between A and B = 13 units
Most Upvoted Answer
If the distance between the points (p, – 5) and (2, 7) is 13 uni...
Explanation:
Let point A be (p,−5) and point B (2, 7) and distance between A and B = 13 units
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Community Answer
If the distance between the points (p, – 5) and (2, 7) is 13 uni...
To find the value of p, we need to use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the points are (p, 5) and (2, 7). We are given that the distance between these points is 13 units. So, we can substitute the values into the formula and solve for p.
Distance Formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given Points:
(x1, y1) = (p, 5)
(x2, y2) = (2, 7)
d = 13
Substituting the values into the formula:
13 = sqrt((2 - p)^2 + (7 - 5)^2)
Simplifying the equation:
169 = (2 - p)^2 + 4
169 = 4 - 4p + p^2 + 4
169 = p^2 - 4p + 8
Rearranging the equation:
p^2 - 4p - 161 = 0
Now, we can solve this quadratic equation to find the value of p. We can factorize the equation or use the quadratic formula. Let's use the quadratic formula:
Quadratic Formula:
p = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -4, and c = -161.
p = (-(-4) ± sqrt((-4)^2 - 4(1)(-161))) / (2(1))
p = (4 ± sqrt(16 + 644)) / 2
p = (4 ± sqrt(660)) / 2
p = (4 ± 2sqrt(165)) / 2
p = 2 ± sqrt(165)
Since p is a real number, we can disregard the negative value. Therefore, the value of p is:
p = 2 + sqrt(165)
However, none of the given options match this value. So, it seems there may be an error in the question or options provided.
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the points are (p, 5) and (2, 7). We are given that the distance between these points is 13 units. So, we can substitute the values into the formula and solve for p.
Distance Formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given Points:
(x1, y1) = (p, 5)
(x2, y2) = (2, 7)
d = 13
Substituting the values into the formula:
13 = sqrt((2 - p)^2 + (7 - 5)^2)
Simplifying the equation:
169 = (2 - p)^2 + 4
169 = 4 - 4p + p^2 + 4
169 = p^2 - 4p + 8
Rearranging the equation:
p^2 - 4p - 161 = 0
Now, we can solve this quadratic equation to find the value of p. We can factorize the equation or use the quadratic formula. Let's use the quadratic formula:
Quadratic Formula:
p = (-b ± sqrt(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -4, and c = -161.
p = (-(-4) ± sqrt((-4)^2 - 4(1)(-161))) / (2(1))
p = (4 ± sqrt(16 + 644)) / 2
p = (4 ± sqrt(660)) / 2
p = (4 ± 2sqrt(165)) / 2
p = 2 ± sqrt(165)
Since p is a real number, we can disregard the negative value. Therefore, the value of p is:
p = 2 + sqrt(165)
However, none of the given options match this value. So, it seems there may be an error in the question or options provided.
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If the distance between the points (p, – 5) and (2, 7) is 13 units, then the value of ‘p’ isa)– 3, 7b)3, – 7c)– 3, – 7d)3, 7Correct answer is option 'A'. Can you explain this answer?
Question Description
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