Quadrilateral ABCD has both reflection and rotation symmetry. What type of quadrilateral could it be? Show or explain.

Rhombus

Step-by-step explanation:

So if |AB| = |BC| then ABCD is a rhombus and has a second line of reflective symmetry, namely \overleftrightarrow{BD}. Quadrilateral ABCD is what is called a kite.

Since ℓ contains two vertices of ABCD the other two must be reflections of one another about ℓ. In the picture ℓ goes through A and C and D=rℓ(B). So rℓ interchanges AD¯¯¯¯¯¯¯¯ and AB¯¯¯¯¯¯¯¯ and also interchanges CB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯. So if |AB|=|BC| then ABCD is a rhombus and has a second line of reflective symmetry, namely BD←→. Quadrilateral ABCD is what is called a kite. Note that we have implicitly used the fact that ABCD is convex: without this hypothesis, the vertex C could be reflected over BD←→, giving a non convex quadrilateral with exactly one line of symmetry.

12

step-by-step explanation:

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough