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The base of an equilateral triangle ABC lies on the y – axis. The co – ordinates of the point C is (0, – 3). If origin is the midpoint of BC, then the co – ordinates of B are
- a)(0, 3)
- b)(3, 0)
- c)( – 3, 0)
- d)(0, – 3)
Correct answer is option 'A'. Can you explain this answer?
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The base of an equilateral triangle ABC lies on the y – axis. Th...
By Pythagorean theorem, we know,
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The base of an equilateral triangle ABC lies on the y – axis. Th...
Given:
- The base of an equilateral triangle ABC lies on the y-axis.
- The coordinates of point C are (0, 3).
- The origin is the midpoint of BC.
To find:
The coordinates of point B.
Solution:
Since the base of the equilateral triangle lies on the y-axis, the x-coordinate of point B will be 0.
Step 1: Find the midpoint of BC.
Since the origin is the midpoint of BC, we can find the coordinates of the midpoint using the midpoint formula.
Let the coordinates of point B be (x, y).
The coordinates of the midpoint M can be found using the formula:
\[M = \left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)\]
Substituting the given values, we have:
\[M = \left(\frac{{0 + 0}}{2}, \frac{{0 + 3}}{2}\right)\]
Simplifying, we get:
\[M = \left(0, \frac{3}{2}\right)\]
Step 2: Use the midpoint to find the coordinates of B.
Since the origin is the midpoint of BC, the coordinates of B will be the negative of the coordinates of M.
Therefore, the coordinates of point B are (0, -3/2).
Final Answer:
The coordinates of point B are (0, -3/2).
- The base of an equilateral triangle ABC lies on the y-axis.
- The coordinates of point C are (0, 3).
- The origin is the midpoint of BC.
To find:
The coordinates of point B.
Solution:
Since the base of the equilateral triangle lies on the y-axis, the x-coordinate of point B will be 0.
Step 1: Find the midpoint of BC.
Since the origin is the midpoint of BC, we can find the coordinates of the midpoint using the midpoint formula.
Let the coordinates of point B be (x, y).
The coordinates of the midpoint M can be found using the formula:
\[M = \left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)\]
Substituting the given values, we have:
\[M = \left(\frac{{0 + 0}}{2}, \frac{{0 + 3}}{2}\right)\]
Simplifying, we get:
\[M = \left(0, \frac{3}{2}\right)\]
Step 2: Use the midpoint to find the coordinates of B.
Since the origin is the midpoint of BC, the coordinates of B will be the negative of the coordinates of M.
Therefore, the coordinates of point B are (0, -3/2).
Final Answer:
The coordinates of point B are (0, -3/2).
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The base of an equilateral triangle ABC lies on the y – axis. Th...
Explanation:
Let the coordinate of B be (0,a).
It is given that (0, 0) is the mid-point of BC.
It is given that (0, 0) is the mid-point of BC.
Therefore 0 = (0 + 0) /2 , 0 =(a - 3) /2 a - 3 = 0 , a = 3
Therefore, the coordinates of B are (0, 3).
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The base of an equilateral triangle ABC lies on the y – axis. The co – ordinates of the point C is (0, – 3). If origin is the midpoint of BC, then the co – ordinates of B area)(0, 3)b)(3, 0)c)( – 3, 0)d)(0, – 3)Correct answer is option 'A'. Can you explain this answer?
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