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If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex is
- a)(4, 7)
- b)(-4, -7)
- c)(4, -7)
- d)(-4, 7)
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre...
Let the third vertex C be (x1. y1) since 0(0, 0) is the orthocenter
⇒ x1 = - 4
y1 = - 7
Hence the third vertex is
(-4, -7)
⇒ x1 = - 4
y1 = - 7
Hence the third vertex is
(-4, -7)
Most Upvoted Answer
If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre...
Given Information:
- Two vertices of the triangle: A(5, -1) and B(-2, 3)
- Orthocentre of the triangle is at the origin (0, 0)
Solution:
Finding the third vertex:
1. The orthocentre of a triangle is the point of intersection of its altitudes.
2. The altitude of a triangle is a line segment from a vertex perpendicular to the line containing the opposite side.
3. To find the third vertex, we need to find the altitude from each of the given vertices A and B and see where they intersect.
Finding the altitude from vertex A:
4. The slope of the line passing through A(5, -1) and the orthocentre (0, 0) is -1/5 (negative reciprocal of the slope of line AB).
5. The equation of the altitude passing through A is y = -1/5*x.
Finding the altitude from vertex B:
6. The slope of the line passing through B(-2, 3) and the orthocentre (0, 0) is -3/2 (negative reciprocal of the slope of line AB).
7. The equation of the altitude passing through B is y = -3/2*x.
Intersection point of the altitudes:
8. Solving the equations of the two altitudes (y = -1/5*x and y = -3/2*x), we get x = -4 and y = -6.
9. Therefore, the third vertex is (-4, -6), which corresponds to option 'B' (-4, -7).
Therefore, the correct answer is option 'B' (-4, -7).
- Two vertices of the triangle: A(5, -1) and B(-2, 3)
- Orthocentre of the triangle is at the origin (0, 0)
Solution:
Finding the third vertex:
1. The orthocentre of a triangle is the point of intersection of its altitudes.
2. The altitude of a triangle is a line segment from a vertex perpendicular to the line containing the opposite side.
3. To find the third vertex, we need to find the altitude from each of the given vertices A and B and see where they intersect.
Finding the altitude from vertex A:
4. The slope of the line passing through A(5, -1) and the orthocentre (0, 0) is -1/5 (negative reciprocal of the slope of line AB).
5. The equation of the altitude passing through A is y = -1/5*x.
Finding the altitude from vertex B:
6. The slope of the line passing through B(-2, 3) and the orthocentre (0, 0) is -3/2 (negative reciprocal of the slope of line AB).
7. The equation of the altitude passing through B is y = -3/2*x.
Intersection point of the altitudes:
8. Solving the equations of the two altitudes (y = -1/5*x and y = -3/2*x), we get x = -4 and y = -6.
9. Therefore, the third vertex is (-4, -6), which corresponds to option 'B' (-4, -7).
Therefore, the correct answer is option 'B' (-4, -7).
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If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. Can you explain this answer?
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