The coordinates of a right triangle are A(5,−1) , B(5,−6) , and C(1,−6) . If that triangle is reflected over the y -axis, what are the coordinates of the reflected triangle? (2 points)
The coordinate of point A becomes ([ ]).
The coordinate of point B becomes ([ ]).
The coordinate of point C becomes ([ ]).
The coordinates of the reflected triangle will be:
A'(-5, -1)
B'(-5, -6)
C'(-1, -6)
The coordinates of a rectangle are (−1,3) , (−1,5) , (−9,5) , and (−9,3) . When that rectangle is reflected over the x -axis, 3 of its coordinates are (−1,−3) , (−1,−5) , and (−9,−5) . What are the coordinates of the reflected rectangle’s missing point?(1 point)
([ ])
The coordinates of the missing point of the reflected rectangle will be (-9, -3).
Leopold draws a quadrilateral with two equal angles, Angles 1 and 2. Angle 3 measures 170 degrees, and Angle 4 measures either 55 degrees less than Angle 3 or 55 degrees more than Angle 3. Determine the angle measurement of Angle 2. Show all work. (4 points)
Let's consider the information provided:
1. Angles 1 and 2 are equal.
2. Angle 3 measures 170 degrees.
3. Angle 4 measures either 55 degrees less than Angle 3 or 55 degrees more than Angle 3.
Given that Angles 1 and 2 are equal, we know they have the same measurement. Let's represent the measurement of Angles 1 and 2 as x degrees.
So, we have:
Angle 1 = x degrees
Angle 2 = x degrees
Angle 3 = 170 degrees
Now, for Angle 4:
Angle 4 is either 55 degrees less than Angle 3 or 55 degrees more than Angle 3. Let's consider both cases:
Case 1: Angle 4 is 55 degrees less than Angle 3:
Angle 4 = Angle 3 - 55
Angle 4 = 170 - 55
Angle 4 = 115 degrees
Case 2: Angle 4 is 55 degrees more than Angle 3:
Angle 4 = Angle 3 + 55
Angle 4 = 170 + 55
Angle 4 = 225 degrees
Since we have two possible values for Angle 4 based on the information given, and the sum of interior angles of a quadrilateral is always 360 degrees, we can calculate the measurement of the remaining angle:
Sum of angles in a quadrilateral = 360 degrees
x + x + 170 + Angle 4 = 360
2x + 170 + 115 = 360
2x + 285 = 360
2x = 75
x = 37.5
Therefore, the measure of Angle 2 is 37.5 degrees.
Verbage
Given:
- Angles 1 and 2 are equal, so let's represent them as x degrees each.
- Angle 3 measures 170 degrees.
- Angle 4 is either 55 degrees less than Angle 3 or 55 degrees more than Angle 3.
Since Angles 1 and 2 are equal, we can set up the equations:
Angle 1 = x degrees
Angle 2 = x degrees
Given that the sum of the interior angles of a quadrilateral is always 360 degrees, we can find Angle 4:
Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360
2x + 170 + Angle 4 = 360
Angle 4 = 360 - 2x - 170
Angle 4 = 190 - 2x
Now, from the information given, Angle 4 is either 55 degrees less or 55 degrees more than Angle 3:
Angle 4 = Angle 3 ± 55
Since Angle 3 is 170 degrees:
190 - 2x = 170 ± 55
190 - 2x = 170 + 55 or 190 - 2x = 170 - 55
Solving for x:
190 - 2x = 225 or 190 - 2x = 115
-2x = 35 or -2x = -75
x = -17.5 or x = 37.5
Since angle measurements cannot be negative, x can only be 37.5 degrees. Therefore, the measure of Angle 2 is 37.5 degrees.