Answer:
We need the following three rigid motions:
i) Reflection around y-axis, ii) Translation three units in the -y direction, iii) Translation four units in the -x direction.
Step-by-step explanation:
We need to perform three operations on pentagon ABCDE to create pentagon A'B'C'D'E':
i) Reflection around y-axis:
(Eq. 1)
ii) Translation three units in the -y direction:
(Eq. 2)
iii) Translation four units in the -x direction:
(Eq. 3)
We proceed to proof the effectiveness of operations defined above by testing point D:
1) 
Given.
2) 
By (Eq. 1)
3) 
By (Eq. 2)
4) 
By (Eq. 3)/Result
Complete the square for the given equation
x² - 2x + ____ + y² - 2y + _____ = 98
x² - 2x + (1) + y² - 2y + (1) = 98 + (1) + (1)
(x - 1)² + (x - 1)² = 100
(x - 1)² + (x - 1)² = 10²
Now the equation is in the form (x - h)² + (y - k)² = r²
Radius = 10
<u>Answer:</u>
The line equation that passes through the given points is 7x – y = 13
<u>Explanation:</u>
Given:
Two points are A(2, 1) and B(3, 8).
To find:
The line equation that passes through the given two points.
Solution:
We know that, general equation of a line passing through two points (x1, y1), (x2, y2) in point slope form is given by
..........(1)
here, in our problem x1 = 3, y1 = 8, x2 = 2 and y2 = 1.
Now substitute the values in (1)
y – 8 = 7(x – 3)
y – 8 = 7x – 21
7x – y = 21 – 8
7x – y = 13
Hence, the line equation that passes through the given points is 7x – y = 13
