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A point R with x-coordinate 1 lies on the line segment joining the points P(-2, 3,5) and Q (7, 0, -1). The coordinates of the point R are
- a)(1,-2,3)
- b)(-1,2,3)
- c)(-1,-2,-3)
- d)(1,2,3)
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A point R with x-coordinate 1 lies on the line segment joining the poi...
The coordinates of points P and Q are given as P(2,−3,5) and (7,0,-1)
Let R divide line segment PQ in the ratio k:1
Hence by section formula, the coordinates of point R are given by,
(k(7)+2/k+1,k(0)−3/k+1, k(-1)+5/k+1)
=(7k+2/k+1, −3/k+1, -1k+5/k+1)
It is given that the x-coordinate of point R is 1.
∴ 7k+2/k+1=1
⇒ 7k+2=k+1
⇒ 6k=-1
⇒ k=-1/6
Hence the coordinates of R are (1,2,3).
Let R divide line segment PQ in the ratio k:1
Hence by section formula, the coordinates of point R are given by,
(k(7)+2/k+1,k(0)−3/k+1, k(-1)+5/k+1)
=(7k+2/k+1, −3/k+1, -1k+5/k+1)
It is given that the x-coordinate of point R is 1.
∴ 7k+2/k+1=1
⇒ 7k+2=k+1
⇒ 6k=-1
⇒ k=-1/6
Hence the coordinates of R are (1,2,3).
Most Upvoted Answer
A point R with x-coordinate 1 lies on the line segment joining the poi...
Given Information:
- Point R has x-coordinate 1.
- Point P is (-2, 3, 5).
- Point Q is (7, 0, -1).
Finding point R:
- Since point R lies on the line segment joining points P and Q, it will have coordinates in the form (1, y, z).
- By using the formula for finding a point on a line segment, we can find the y and z coordinates of point R.
Calculating y-coordinate of R:
- Using the formula for finding the y-coordinate of point R, we get:
y = y1 + (x - x1) * ((y2 - y1) / (x2 - x1))
y = 3 + (1 - (-2)) * ((0 - 3) / (7 - (-2)))
y = 3 + 3 * (-3 / 9)
y = 3 - 1
y = 2
Calculating z-coordinate of R:
- Using the formula for finding the z-coordinate of point R, we get:
z = z1 + (x - x1) * ((z2 - z1) / (x2 - x1))
z = 5 + (1 - (-2)) * ((-1 - 5) / (7 - (-2)))
z = 5 + 3 * (-6 / 9)
z = 5 - 2
z = 3
Coordinates of point R:
- Therefore, the coordinates of point R are (1, 2, 3).
Correct Answer:
- The correct option is (D) (1, 2, 3).
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A point R with x-coordinate 1 lies on the line segment joining the points P(-2, 3,5) and Q (7, 0, -1). The coordinates of the point R area)(1,-2,3)b)(-1,2,3)c)(-1,-2,-3)d)(1,2,3)Correct answer is option 'D'. Can you explain this answer?
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