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The line segment joining the points P(3,3)and Q(6,-6)is trisected at the points AandB such that A is nearer to P .if A also lies on the line given by 2x+y+k=0,find the value of k.
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Most Upvoted Answer
The line segment joining the points P(3,3)and Q(6,-6)is trisected at t...
We have P(3, 3) and Q(6, -6) Let coordinates of A is (x₁, y₁) and that of B is (x₂, y₂)..Now, point A divides the line PQ in the ratio 1:2 By section formula,... ⇒ x₁ = {(2 × 3) + (1 × 6)}/(2+1)⇒ x₁ = 4⇒ y₁ = {(2 × 3) + (1 × -6)}/(2+1)⇒ y₁ = 0 also, point A lies on the line 2x + y + k = 0, ...⇒ (2 × 4) + 0 + k = 0⇒ k = -8 So thats your answer.. Thank u..
Community Answer
The line segment joining the points P(3,3)and Q(6,-6)is trisected at t...
Solution:
Given:
- Points P(3,3) and Q(6,-6)
- The line segment joining P and Q is trisected at points A and B
- Point A is nearer to P
- Point A lies on the line given by 2x + y + k = 0
To find the value of k, we need to determine the coordinates of points A and B.
Step 1: Finding the coordinates of point A
Since the line segment PQ is trisected, we can divide it into three equal parts. Let's denote the coordinates of point A as (x1, y1) and point B as (x2, y2).
Using the section formula, we can find the coordinates of point A:
x1 = (2 * xP + 1 * xQ) / 3
y1 = (2 * yP + 1 * yQ) / 3
Substituting the coordinates of P(3,3) and Q(6,-6) into the formulas:
x1 = (2 * 3 + 1 * 6) / 3 = 4
y1 = (2 * 3 + 1 * -6) / 3 = 1
Therefore, the coordinates of point A are (4, 1).
Step 2: Checking if point A lies on the given line
We are given that point A lies on the line 2x + y + k = 0. Substituting the coordinates of A(4, 1) into the equation:
2 * 4 + 1 + k = 0
8 + 1 + k = 0
9 + k = 0
k = -9
Therefore, the value of k is -9.
Conclusion:
The value of k is -9. Point A lies on the line 2x + y - 9 = 0.
Given:
- Points P(3,3) and Q(6,-6)
- The line segment joining P and Q is trisected at points A and B
- Point A is nearer to P
- Point A lies on the line given by 2x + y + k = 0
To find the value of k, we need to determine the coordinates of points A and B.
Step 1: Finding the coordinates of point A
Since the line segment PQ is trisected, we can divide it into three equal parts. Let's denote the coordinates of point A as (x1, y1) and point B as (x2, y2).
Using the section formula, we can find the coordinates of point A:
x1 = (2 * xP + 1 * xQ) / 3
y1 = (2 * yP + 1 * yQ) / 3
Substituting the coordinates of P(3,3) and Q(6,-6) into the formulas:
x1 = (2 * 3 + 1 * 6) / 3 = 4
y1 = (2 * 3 + 1 * -6) / 3 = 1
Therefore, the coordinates of point A are (4, 1).
Step 2: Checking if point A lies on the given line
We are given that point A lies on the line 2x + y + k = 0. Substituting the coordinates of A(4, 1) into the equation:
2 * 4 + 1 + k = 0
8 + 1 + k = 0
9 + k = 0
k = -9
Therefore, the value of k is -9.
Conclusion:
The value of k is -9. Point A lies on the line 2x + y - 9 = 0.
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The line segment joining the points P(3,3)and Q(6,-6)is trisected at the points AandB such that A is nearer to P .if A also lies on the line given by 2x+y+k=0,find the value of k.?
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The line segment joining the points P(3,3)and Q(6,-6)is trisected at the points AandB such that A is nearer to P .if A also lies on the line given by 2x+y+k=0,find the value of k.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The line segment joining the points P(3,3)and Q(6,-6)is trisected at the points AandB such that A is nearer to P .if A also lies on the line given by 2x+y+k=0,find the value of k.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The line segment joining the points P(3,3)and Q(6,-6)is trisected at the points AandB such that A is nearer to P .if A also lies on the line given by 2x+y+k=0,find the value of k.?.
The line segment joining the points P(3,3)and Q(6,-6)is trisected at the points AandB such that A is nearer to P .if A also lies on the line given by 2x+y+k=0,find the value of k.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The line segment joining the points P(3,3)and Q(6,-6)is trisected at the points AandB such that A is nearer to P .if A also lies on the line given by 2x+y+k=0,find the value of k.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The line segment joining the points P(3,3)and Q(6,-6)is trisected at the points AandB such that A is nearer to P .if A also lies on the line given by 2x+y+k=0,find the value of k.?.
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