Step-by-step explanation:
Let the mid-point of BC is M. So, the length of BM = MC.
The coordinates of B are (-6, 1) and coordinates of C are (5, -1). Therefore, using the distance formula find the distance as follows.
d = [tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}[/tex]
Place the values form points B and C into the above formula as follows.
d = [tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}[/tex]
= [tex]\sqrt{(5- (-6))^{2} + ((-1)- (1))^{2}}[/tex]
= [tex]\sqrt{(11)^{2} + (-2)^{2}}[/tex]
= [tex]\sqrt{121 + 4}[/tex]
= [tex]\sqrt{125}[/tex]
= 11.18 (approx)
Therefore, the length of mid-point of line segment will be [tex]\frac{11.18}{2}[/tex] = 5.59 (approx). BM = MC = 5.59.
The length of line segment which is parallel to BC = [tex]\frac{d}{2}[/tex].
