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Posing A(-4,2) is reflected over the line x= 3 to create the point A’. What are the coordinates of A
1 answer:
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Write the polynomial as an equation.
y
=
x
3
−
2
x
2
−
3
x
+
6
y
=
x
3
-
2
x
2
-
3
x
+
6
To find the roots of the equation, replace
y
y
with
0
0
and solve.
0
=
x
3
−
2
x
2
−
3
x
+
6
0
=
x
3
-
2
x
2
-
3
x
+
6
Replace
y
y
with
0
0
and solve for
x
x
.
Tap for more steps...
x
=
2
,
√
3
,
−
√
3
x
=
2
,
3
,
-
3
The result can be shown in multiple forms.
Exact Form:
x
=
2
,
√
3
,
−
√
3
x
=
2
,
3
,
-
3
Decimal Form:
x
=
2
,
1.73205080
…
,
−
1.73205080
…
y
=
x
3
−
2
x
2
−
3
x
+
6
y
=
x
3
-
2
x
2
-
3
x
+
6
To find the roots of the equation, replace
y
y
with
0
0
and solve.
0
=
x
3
−
2
x
2
−
3
x
+
6
0
=
x
3
-
2
x
2
-
3
x
+
6
Replace
y
y
with
0
0
and solve for
x
x
.
Tap for more steps...
x
=
2
,
√
3
,
−
√
3
x
=
2
,
3
,
-
3
The result can be shown in multiple forms.
Exact Form:
x
=
2
,
√
3
,
−
√
3
x
=
2
,
3
,
-
3
Decimal Form:
x
=
2
,
1.73205080
…
,
−
1.73205080
…
Please note that dilation does not affect angles. Thus, if an image is dilated the angle remains the same and does not change.
Therefore, even if is dilated to
by a factor of 1.5 (or by any factor for that matter), the linear dimensions of the original triangle
will either get stretched or get shrunk by a factor of 1.5 but the angles of the original triangle will not be affected in any case.
Please note that this is true for all two dimensional geometric shapes.