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The midpoints pf the sides BC, CA,and AB of triangle ABC are D(3,4) E(8,9) and F(6,7). Find the coordinates of the vertices of the triangle?
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The midpoints pf the sides BC, CA,and AB of triangle ABC are D(3,4) E(...
Given:
The midpoints of the sides BC, CA, and AB of triangle ABC are D(3,4), E(8,9), and F(6,7) respectively.

To Find:
The coordinates of the vertices of the triangle.

Approach:
To find the coordinates of the vertices, we can use the concept of midpoints. The midpoint of a line segment is the average of the coordinates of its endpoints. Using this concept, we can find the coordinates of the vertices by finding the average of the coordinates of the midpoints.

Solution:

Step 1: Finding the coordinates of vertex A:
To find the coordinates of vertex A, we need to find the average of the coordinates of midpoints D and E.

x-coordinate of A = (x-coordinate of D + x-coordinate of E) / 2 = (3 + 8) / 2 = 11 / 2 = 5.5
y-coordinate of A = (y-coordinate of D + y-coordinate of E) / 2 = (4 + 9) / 2 = 13 / 2 = 6.5

Therefore, the coordinates of vertex A are (5.5, 6.5).

Step 2: Finding the coordinates of vertex B:
To find the coordinates of vertex B, we need to find the average of the coordinates of midpoints C and F.

x-coordinate of B = (x-coordinate of C + x-coordinate of F) / 2
y-coordinate of B = (y-coordinate of C + y-coordinate of F) / 2

However, we do not have the coordinates of midpoint C. To find it, we can use the fact that the midpoint of a line segment is the average of the coordinates of its endpoints. So, the coordinates of midpoint C can be found as:

x-coordinate of C = (x-coordinate of D + x-coordinate of E) / 2 = (3 + 8) / 2 = 11 / 2 = 5.5
y-coordinate of C = (y-coordinate of D + y-coordinate of E) / 2 = (4 + 9) / 2 = 13 / 2 = 6.5

Now we can find the coordinates of vertex B:

x-coordinate of B = (x-coordinate of C + x-coordinate of F) / 2 = (5.5 + 6) / 2 = 11.5 / 2 = 5.75
y-coordinate of B = (y-coordinate of C + y-coordinate of F) / 2 = (6.5 + 7) / 2 = 13.5 / 2 = 6.75

Therefore, the coordinates of vertex B are (5.75, 6.75).

Step 3: Finding the coordinates of vertex C:
To find the coordinates of vertex C, we need to find the average of the coordinates of midpoints D and F.

x-coordinate of C = (x-coordinate of D + x-coordinate of F) / 2 = (3 + 6) / 2 = 9 / 2 = 4.5
y-coordinate of C = (y-coordinate of D + y-coordinate of F) / 2 = (4 +
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The midpoints pf the sides BC, CA,and AB of triangle ABC are D(3,4) E(8,9) and F(6,7). Find the coordinates of the vertices of the triangle?
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The midpoints pf the sides BC, CA,and AB of triangle ABC are D(3,4) E(8,9) and F(6,7). Find the coordinates of the vertices of the triangle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The midpoints pf the sides BC, CA,and AB of triangle ABC are D(3,4) E(8,9) and F(6,7). Find the coordinates of the vertices of the triangle? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The midpoints pf the sides BC, CA,and AB of triangle ABC are D(3,4) E(8,9) and F(6,7). Find the coordinates of the vertices of the triangle?.
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