SOLUTION: The vertices of a triangle are A (4,-4), B (10,4) and C (2,6). Find the distance from the vertex to the midpoint of the opposite side

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Question 1004833: The vertices of a triangle are A (4,-4), B (10,4) and C (2,6). Find the distance from the vertex to the midpoint of the opposite side
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
given:
The vertices of a triangle are:
A (,), B (,) and C (,)
plot the points and draw a triangle:

if the vertex , the opposite side is
so, find the midpoint of the opposite side
Solved by pluggable solver: Midpoint


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (4, -4), we can say (x1, y1) = (4, -4)
So ,


Since the second point is (10, 4), we can also say (x2, y2) = (10, 4)
So ,


Put this all together to get: , , , and

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Finding the x coordinate of the midpoint: Add up the corresponding x coordinates x1 and x2 and divide that sum by 2


X Coordinate of Midpoint =


X Coordinate of Midpoint =


X Coordinate of Midpoint =


X Coordinate of Midpoint =



So the x coordinate of the midpoint is 7


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Finding the y coordinate of the midpoint: Add up the corresponding y coordinates y1 and y2 and divide that sum by 2


Y Coordinate of Midpoint =


Y Coordinate of Midpoint =


Y Coordinate of Midpoint =


Y Coordinate of Midpoint =


So the y coordinate of the midpoint is 0



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Summary:


The midpoint of the segment joining the two points (4, -4) and (10, 4) is (7, 0).


So the answer is (7, 0)




the midpoint is at (,) and C is at (,)
find the distance between these two points:

Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (7, 0), we can say (x1, y1) = (7, 0)
So ,


Since the second point is (2, 6), we can also say (x2, y2) = (2, 6)
So ,


Put this all together to get: , , , and

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Now use the distance formula to find the distance between the two points (7, 0) and (2, 6)






Plug in , , , and













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Answer:


The distance between the two points (7, 0) and (2, 6) is exactly units


The approximate distance between the two points is about 7.81024967590665 units



So again,


Exact Distance: units


Approximate Distance: units







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