What is the equation of a line that is perpendicular to - x + 2y = 4 and passes through the point (-2,1)

1 answer:

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Perpendicular has slope that multiplies to -1

the slope for ax+by=c is -a/b
-1x+2y=4
slope=-(-1)/2=1/2
1/2 times what=-1?
-2

y=mx+b
m=slope
we need slope is -2
y=-2x+b
find b
given
(-2,1)
(x,y)
x=-2 and y=1 is a solution

1=-2(-2)+b
1=4+b
mius 4 both sides
-3=b

y=-2x-3 is equation

first one

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In a word processing document or on a separate piece of paper, use the guide to construct a two-column proof proving AC > EF

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Answer:

Complete proof is written below.

Facts and explanation about the segments shown in question :

As BC = EF is a given statement in the question
AB + BC = AC because the definition of betweenness gives us a clear idea that if a point B is between points A and C, then the length of AB and the length of BC is equal to the length of AC. Also according to Segment addition postulate, AB + BC = AC. For example, if AB = 5 and BC= 7 then AC = AB + BC → AC = 12
AC > BC because the Parts Theorem (Segments) mentions that if B is a point on AC between A and C, then AC > BC and AC>AB. So, if we observe the question figure, we can realize that point B lies on the segment AC between points A and C.
AC > EF because BC is equal to EF and if AC>BC, then it must be true that the length of AC must greater than the length segment EF.

Below is the complete proof of the observation given in the question:

STATEMENT REASON 

___________________________________________________

1. BC = EF 1. Given

2. AB + BC = AC 2. Betweenness

3. AC > BC 3. Def. of segment inequality

4. AC > EF 4. Def. of congruent segments

Keywords: statement, length, reason, proof

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