Answer:
<em>k = - 7.5 </em>
Step-by-step explanation:
Slope "m" of a line through points
( ,
)
( ,
)
is m =
Slopes of perpendicular lines are opposite reciprocal:
= - 1
~~~~~~~~~~~~~~~
The slope of a line through points (0, 7) and (2, 10)
=
=
Slope of perpendicular line through points (3, 5) and (k, 12) is =
or =
=
2(k - 3) = - 21
k - 3 = - 10.5
<em>k = - 7.5</em>
Linear pair angles, which are angles that together form a straight line are
supplementary angles.
The one that completed the proof incorrectly is <u>Becky</u>.
Reasons:
The two column proof is presented as follows;
Statement Reason
1. Segment GH intersects segment AB at K 1. Given
2. m∠AKG + m∠HKB = 180° 2.Definition of Supplementary Angles
m∠GKB + m∠HKB = 180°
3. m∠AKG + m∠HKB = m∠GKB + m∠HKB 3. Substitution property
4. m∠AKG = m∠HKB 4. Subtraction Property
The difference between Angie's Proof and Becky's Proof is in Statement 2.
Becky's proof is incorrect because the measure of angles m∠AKG and
m∠HKB and m∠GKB and m∠HKB are not given, therefore, the use of the
reason of Angle Addition Postulate in statement 2. is incorrect.
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