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Question
If the coordinates of the sides AB and AC of ∆ABC are (3, 5) and (−3, −3), respectively, then write the length of side BC.
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Solution
Disclaimer: In the question it should have been the coordinates of the mid points of AB and AC are (3, 5) and (-3, -3) 
Given: the coordinates of the midpoints of AB and AC are (3,5) and (-3, -3).
Let, D and E be the midpoints of AB and AC, respectively.
\[\therefore DE = \sqrt{\left[ 3 - \left( - 3 \right) \right]^2 + \left[ 5 - \left( - 3 \right) \right]^2}\]
\[ = \sqrt{6^2 + 8^2}\]
\[ = \sqrt{100}\]
= 10 units
Now, as D and E are midpoints of AB and AC respectively,
by the mid-points theorem,
\[BC = 2 \times DE\]
= 2 x 10 units
= 20 units
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