Response
The coordinates for line PQ are (-8,2) and (4,2)
The slope of this line is
Coordinates for line MN are (8,-6) and (8,-8)
The slope of this line is
Line PQ runs parallel to the x-axis, intersecting at y = 2.
Line MN runs parallel to the y-axis, intersecting at x = 8.
Both lines intersect at the point (8,2).
Response:
PQ's slope is 0
MN's slope equals infinity
The lines PQ and MN are perpendicular to one another
Detailed explanation:
For two points in the coordinate plane, denoted as (x1, y1) and (x2, y2), the slope is determined as follows:
If a line has a slope of zero, it runs parallel to the X-axis and stands perpendicular to the Y-axis
If a line's slope is infinite, it is parallel to the Y-axis and perpendicular to the X-axis
Moreover, it is established that X and Y are perpendicular to each other.
As PQ's slope is zero, it runs parallel to the X-axis and perpendicular to the Y-axis
With MN having an infinite slope, it runs parallel to the Y-axis and perpendicular to the X-axis.
Therefore, lines PQ and MN are indeed perpendicular.
For the function
and
both yield the same result.
Detailed breakdown:
The functions involved are
Step 1:
Insert in
to find the value of
.
Insert in
to find the value of
.
Step 2:
Insert in
to obtain the value of
.
Step 3:
Replace in
to find the value of
.
Step 4:
Insert in
to find the value of
.
Also, replace in
to obtain the value of
.
Step 5:
Insert in
to obtain the value of
.
Replace in
to find the value of
.
Step 6:
Insert into
to find the value of
.
Also, substitute in
to obtain the value of
.
Step 7:
According to the provided condition .
(a). Insert and
into the previously mentioned equation.
(b). Multiply through by on both sides.
(c). Move the term to the left side of the equation.
(d). Divide the middle term so that its sum equals 5 and the product equals 6.
From the analysis above, it is noted that for both functions
and
yield the same outcome.
Using a direct approach:
The table representing function and
is included below.
For more information:
1. What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? (0,–6) (0,12) (–8,0) (2,0)