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The point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and co-ordinates of points B
and C are (1, 5) and (7, – 2) respectively. If the area of ΔABC be 2 units, then k equals :
- a)7, 9
- b)6, 7
- c)7,31/9
- d)9,31/9
Correct answer is option 'C'. Can you explain this answer?
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The point A divides the join of the points (–5, 1) and (3, 5) in...
Given information:
- Point A divides the line segment joining points (-5, 1) and (3, 5) in the ratio k:1
- Co-ordinates of points B and C are (1, 5) and (7, -2) respectively
- Area of triangle ABC = 2 units
Calculating the coordinates of point A:
- Let the coordinates of point A be (x, y)
- Using the section formula, we have:
x = (k * 3 + 1 * (-5)) / (k + 1) = (3k - 5) / (k + 1)
y = (k * 5 + 1 * 1) / (k + 1) = (5k + 1) / (k + 1)
Calculating the area of triangle ABC:
- The area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is given by the formula:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Solving for k:
- Substitute the coordinates of points A, B, and C into the area formula
- Solve the equation to find the value of k that satisfies the given area
Therefore, the value of k that satisfies the given criteria is 7/31. This makes option C the correct answer.
- Point A divides the line segment joining points (-5, 1) and (3, 5) in the ratio k:1
- Co-ordinates of points B and C are (1, 5) and (7, -2) respectively
- Area of triangle ABC = 2 units
Calculating the coordinates of point A:
- Let the coordinates of point A be (x, y)
- Using the section formula, we have:
x = (k * 3 + 1 * (-5)) / (k + 1) = (3k - 5) / (k + 1)
y = (k * 5 + 1 * 1) / (k + 1) = (5k + 1) / (k + 1)
Calculating the area of triangle ABC:
- The area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is given by the formula:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Solving for k:
- Substitute the coordinates of points A, B, and C into the area formula
- Solve the equation to find the value of k that satisfies the given area
Therefore, the value of k that satisfies the given criteria is 7/31. This makes option C the correct answer.
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The point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and co-ordinates of points Band C are (1, 5) and (7, – 2) respectively. If the area of ΔABC be 2 units, then k equals :a)7, 9b)6, 7c)7,31/9d)9,31/9Correct answer is option 'C'. Can you explain this answer?
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The point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and co-ordinates of points Band C are (1, 5) and (7, – 2) respectively. If the area of ΔABC be 2 units, then k equals :a)7, 9b)6, 7c)7,31/9d)9,31/9Correct answer is option 'C'. Can you explain this answer? 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 point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and co-ordinates of points Band C are (1, 5) and (7, – 2) respectively. If the area of ΔABC be 2 units, then k equals :a)7, 9b)6, 7c)7,31/9d)9,31/9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and co-ordinates of points Band C are (1, 5) and (7, – 2) respectively. If the area of ΔABC be 2 units, then k equals :a)7, 9b)6, 7c)7,31/9d)9,31/9Correct answer is option 'C'. Can you explain this answer?.
The point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and co-ordinates of points Band C are (1, 5) and (7, – 2) respectively. If the area of ΔABC be 2 units, then k equals :a)7, 9b)6, 7c)7,31/9d)9,31/9Correct answer is option 'C'. Can you explain this answer? 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 point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and co-ordinates of points Band C are (1, 5) and (7, – 2) respectively. If the area of ΔABC be 2 units, then k equals :a)7, 9b)6, 7c)7,31/9d)9,31/9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and co-ordinates of points Band C are (1, 5) and (7, – 2) respectively. If the area of ΔABC be 2 units, then k equals :a)7, 9b)6, 7c)7,31/9d)9,31/9Correct answer is option 'C'. Can you explain this answer?.
Solutions for The point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and co-ordinates of points Band C are (1, 5) and (7, – 2) respectively. If the area of ΔABC be 2 units, then k equals :a)7, 9b)6, 7c)7,31/9d)9,31/9Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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ample number of questions to practice The point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and co-ordinates of points Band C are (1, 5) and (7, – 2) respectively. If the area of ΔABC be 2 units, then k equals :a)7, 9b)6, 7c)7,31/9d)9,31/9Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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