1)The sum of angles in a triangle is 180°
To find the value of x, we sum all the angles in the triangle and equate to 180°.
[tex]x + 37 + 36 = 180[/tex]
[tex]x + 73 = 180[/tex]
Subtract 73 from both sides
[tex]x = 180 - 73[/tex]
[tex]x = 107 \degree[/tex]
Therefore the triangle is obtuse.
Answer: C) 107°, obtuse
2) To find the rule of the transformation, we analyze the coordinates of the preimage and the image
[tex](3,-5)\to(3-1,-5-3)\to (2,-8)[/tex]
[tex](5,1)\to(5-1,1-3)\to (4,-2)[/tex]
[tex](1,3)\to(1-1,3-3)\to (0,0)[/tex]
[tex]( - 1,1)\to( - 1-1,1-3)\to ( - 2,-2)[/tex]
[tex]( - 1,-4)\to( - 1-1,-4-3)\to ( - 2,-7)[/tex]
So we can see that, each time 1 is subtracted from the first coordinate and 3 is subtracted from the second coordinates to get the image coordinates.
Therefore the rule is:
[tex](x,y)\to(x-1,y-3)[/tex]
Answer: D
3) The given angle is 58°.
Since translation is a rigid motion, the preimage and the image of the angle are congruent.
Therefore the Translated angle measures 58°, because translation preserves angle measure.
The correct answer is C.
Answer: C
4)
4) By vertical angles theorem, <4 is congruent to <6.
<4 and <2 are congruent by corresponding angles property.
<4 and <8 are congruent by alternate interior angles property.
The <7 is not congruent to <4
Answer:C
5) The rule for 90° clockwise rotation about the origin is
[tex](x,y)\to (y,-x)[/tex]
The vertex W of the square has coordinates W(1,5)
After a rotation of 90° clockwise about the origin, the image will be:
[tex]W(1,5)\to \: W'(5,-1)[/tex]
Answer:A
6) The given point is (11,1).
When we translate 10 units down, the new coordinates will be (11,1-10)=(11,-9)
When we reflect over x-axis, we get:
(11,--9)=(11,9). because we negate the y-coordinate.
Answer:A
