Given the vertices of a triangle as A(2, 5), B(4, 6) and C(3, 1).
a.) A transformation, R_x-axis means that the vertices of the rectangle were reflected across the x-axis.
When a point on the coordinate axis is refrected across the x-axis, the sign of the y-coordinate of the point changes.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule R_x-axis are A'(2, -5), B'(4, -6), C'(3, -1)
b.) A transformation, R_y = 3 means that the vertices of the rectangle were reflected across the line y = 3.
When a point on the coordinate axis is refrected across the a horizontal line, the distance of the point from the line is equal to the distance of the image of the point from the line.
Therefore,
the vertices of the triangle A'B'C' resulting from the transformation
of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule are A'(2, 1),
B'(4, 0), C'(3, 5)
c.) A transformation, T<-2, 5> means that the vertices of the rectangle were shifted 2 units to the left and 5 units up.
Therefore,
the vertices of the triangle A'B'C' resulting from the transformation
of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<-2, 5> are A'(0, 10),
B'(2, 11), C'(1, 6).
d.) A transformation, T<3, -6> means that the vertices of the rectangle were shifted 3 units to the right and 6 units down.
Therefore,
the vertices of the triangle A'B'C' resulting from the transformation
of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<3, -6> are A'(5, -1),
B'(7, 0), C'(6, -5).
e.) A transformation, r(90°, o) means that the vertices of the rectangle were rotated 90° to the right about the origin.
When a point on the coordinate axis is rotated about the origin b 90°, the quadrant of the point changes to the right with the x-value and the y-value of the point interchanging.
Therefore,
the vertices of the triangle A'B'C' resulting from the transformation
of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule r(90°, o) are A'(5, -2),
B'(6, -4), C'(1, -3)
Answer:
First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.
For:
x
=
0
y
=
0
+
5
y
=
5
Or
(
0
,
5
)
For:
x
=
−
2
y
=
−
2
+
5
y
=
3
Or
(
−
2
,
3
)
We can now plot the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.
The boundary line will be solid because the inequality operator contains an "or equal to" clause.
graph{(x^2+(y-5)^2-0.125)((x+2)^2+(y-3)^2-0.125)(y-x-5)=0 [-20, 20, -10, 10]}
Now, we can shade the left side of the line.
graph{(y-x-5) >= 0 [-20, 20, -10, 10]}
Angle of depression is the angle that is created below the horizontal with your line of sight. to solve the angle of depression, use the formula:
tan(d) = o / a
where d is the angle of depresion
h is the opposite side of the angle which is the height 60 ft
a is the adjacent side of the angle which is 25 ft
tan( d ) = 60 / 25
d = arctan ( 60 / 25)
d = 67.38 degrees