How do you prove that a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects?
1 answer:
Check the picture drawn
Consider the line segment AB,
let M be the midpoint of AB, so AM=MA
erect the perpendicular MT to AB from point M. Pick a point P on MT and join it to the points A and B
The triangles PMA and PMB are congruent from the Side Angle Side congruence postulate:
AM=MA, PM is common and m(PMA)=m(PMB)=90°, as MT is perpendicular to AB
so PA=PB
Consider the line segment AB,
let M be the midpoint of AB, so AM=MA
erect the perpendicular MT to AB from point M. Pick a point P on MT and join it to the points A and B
The triangles PMA and PMB are congruent from the Side Angle Side congruence postulate:
AM=MA, PM is common and m(PMA)=m(PMB)=90°, as MT is perpendicular to AB
so PA=PB
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Answer:
A, B and C
Step-by-step explanation:
In the equation: 3y=27x
Making y the subject of the equation, we have:
The constant of proportionality between y and x is 9.
We want to determine which relationships have the same constant of proportionality 9.
<u>Option A</u>
y=9x
The constant of proportionality is 9.
<u>Option B</u>
2y=18x
Divide both sides by 2 to obtain: y=9x
The constant of proportionality is 9.
<u>Option C</u>
x=3, y=1/3
Substitution into y=kx gives:
1/3=3k
k=9
The constant of proportionality is 9.
<u>Option D</u>
x=6, y=2/3
Substitution into y=kx gives:
2/3=6k
k=2/3*6=4
The constant of proportionality is 4.
<u>Option E</u>
When x=2, y=18
Substitution into y=kx gives:
18=2k
k=9
However, when x=4, y=27
Substitution into y=kx gives:
27=4k
k=6.75
This is not a proportional relation since the constant of proportionality is not equal.
The correct options are A, B and C