Answer:
See Below.
Step-by-step explanation:
We are given that ∠1 and ∠7 are supplementary.
And we would like to prove that a is parallel to b.
Statements: Reasons:
Given
Supplementary Angles
Definition of Supplementary
Congruent Supplements Theorem
Corresponding Angles Converse
And we are done!
Answer:
Step-by-step explanation:
The point slope form of the equation is expressed as
y - 7/2 = 1/2(x - 4)
Comparing with the point slope form of an equation which is expressed as
y - y1 = m(x - x1)
m represents slope
Therefore
m = 1/2
y1 = 7/2
x1 = 4
The slope intercept form of the equation of a straight line is expressed as
y = mx + c
Where c represents the intercept
Substituting y = 7/2, m = 1/2 and x = 4 into y = mx + c, it becomes
7/2 = 1/2 × 4 + c
7/2 = 2 + c
c = 2 - 7/2 = (4 - 7)/2 = - 3/2
Therefore, the y intercept is - 3/2
Answers:
===================================================
Explanation:
Part (a)
Lines LN and PN have the point N in common. This is the intersection point.
-----------------
Part (b)
To name a plane, pick any three non-collinear points that are inside it. We cannot pick points H, J, K together because infinitely many planes pass through it. Imagine the piece of flat paper able to rotate around this axis (like a propeller). Having the points not all on the same line guarantees we form exactly one unique plane.
I'll pick the non-collinear points P, H and J to get the name Plane PHJ. Other answers are possible.
------------------
Part (c)
Points H, J and K are collinear as they are on the same line. Pick either H or K to fill out the answer box. I'll go with point K
------------------
Part (d)
Point P and line HK are coplanar. They exist in the same flat plane, or on the same sheet of flat paper together.
We can think of that flat plane as the ground level while something like point N is underground somewhere. So point N and anything on that ground plane wouldn't be coplanar.
Note: there are other possible names for line HK such as line JH or line JK. The order doesn't matter when it comes to naming lines.
Half a book each month!!! have a good day!
