
: The distance between the points (4, 3, 7) and (1, -1, -5) is?
(a) 7
(b) 12
(c) 13
(d) 25
Answer
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Hint: Assume (4, 3, 7) as and (1, -1, 5) as . Use distance formula in 3-dimensional geometry given by: , where ‘d’ is the distance between the two points and .
Complete step-by-step answer:
We know that a point lying in any plane is represented by the coordinates . Now, we have been provided with two points (4, 3, 7) and (1, -1, -5) and we have to find the distance between these two.
Let us assume these points as and respectively. Therefore,
and .
Let us assume that the distance between these two points is .
By distance formula, we know that, distance between two points is, . Therefore,
Therefore, the distance between these two points is 13 units.
Hence, option (c) is the correct answer.
Note: One may note that in 2-dimension geometry, we have only two coordinates of a particular point, that is, (x, y) which lies in the x-y plane. The distance between any two points in 2-D space is given by: . Similarly, in 3-D space we have another coordinate in addition to x and y, that is z. This z-coordinate represents that the required point is above or below the x-y plane. So, we use the distance formula, for the calculation of distance between two points, like we did in the above question.
Complete step-by-step answer:
We know that a point lying in any plane is represented by the coordinates
Let us assume these points as
Let us assume that the distance between these two points is
By distance formula, we know that, distance between two points is,
Therefore, the distance between these two points is 13 units.
Hence, option (c) is the correct answer.
Note: One may note that in 2-dimension geometry, we have only two coordinates of a particular point, that is, (x, y) which lies in the x-y plane. The distance between any two points in 2-D space is given by:
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