A line bisector is a straight line that divides a given line into two equal parts. Thus the following steps are required by Naomi to show that point D is equidistant from points A and C.
BD ⊥ AC (given)
BD = 3 units, and AC = 8 units.
BD is the perpendicular bisector of segment AC (given)
Thus,
<BDA ≅ <BDC (right angles formed by a perpendicular bisector)
AD ≅ DC (equal parts of a bisected line)
AD ≅ DC = 4 units
Thus joining points B to A, and B to C,
BA ≅ BC.
So that applying Pythagoras theorem to ΔABD, we have:
[tex]/hyp/^{2}[/tex] = [tex]Adj 1^{2}[/tex] + [tex]Adj 2^{2}[/tex]
[tex]AB^{2}[/tex] = [tex]3^{2}[/tex] + [tex]4^{2}[/tex]
= [tex]\sqrt{25}[/tex]
AB = 5 units
So that,
BA ≅ BC = 5 units
Therefore, it can be concluded that point D is equidistant from points A and C.
For more clarifications on a perpendicular bisector of a line, visit: https://brainly.com/question/929137
#SPJ1
