Answer:
The distance A’C’ is 4.47 units
Step-by-step explanation:
Before we go on, we need to get the appropriate transformation
Mathematically, we have a 90 degrees clockwise rotation yielding the following;
(x,y) to (-y,x)
A is (-4,1)
C is (-2,5)
By transforming, we have
A’( -1,-4)
C’ (-5,-2)
To get the magnitude of the line segment, we are going to use the distance formula between points
We have this as;
D = √(x2-x1)^2 + (y2-y1)^2
D = √(-5-(-1))^2 + (-2-(-4))^2
D = √(-4)^2 + (2)^2
D = √(16 + 4)
D = √20
D = 4.47 units
Answer:
(1,-1)
Step-by-step explanation:
The solution to a system of equation means the x and y values if we were to solve both equations (of lines) simultaneously.
That is also known as the intersecting points.
The top-right part is known as the 1st Quadrant in a coordinate system.
Top-left is 2nd Quadrant.
Bottom left is 3rd Quadrant.
Bottom right is 4th Quadrant.
The values of x and y (positive or negative) of each quadrant is shown below:
- Quadrant 1: x +ve, y +ve
- Quadrant 2: x -ve, y +ve
- Quadrant 3: x -ve, y -ve
- Quadrant 4: x +ve, y -ve
The intersection point (solution) of the 2 lines shown is in the 4th quadrant, which has x values positive and y values negative.
From the answer choices, we see that 3rd answer choice goes with this -- (1,-1), so this is the correct choice.
Let's start by solving the first equation.
a) -3 = 7 + 2t/3
To begin simplifying this equation, we should multiply both sides by 3 to get rid of the denominator on the right side of the equation.
-9 = 7 + 2t
Next, we should subtract 7 from both sides to cancel out the 7 on the right side.
-16 = 2t
Finally, we should divide both sides by 2.
t= -8
Now let's move on to the next equation.
b) 4(5x-2) = 7(2x+3)
Let's use the distributive property to get rid of the parentheses and their coefficients.
20x-8 = 14x + 21
Now, lets subtract 14x from both sides of the equation.
6x - 8 = 21
Next, let's add 8 to both sides of the equation.
6x = 29
And divide both sides by the coefficient of x, which is 6.
x = 29/6 or 4 5/6
Now for the last equation.
C) 2x - 6 = 20 - 2.5x
First, we should add 2.5x to both sides to cancel out the -2.5x on the right side of the equation.
4.5x - 6 = 20
Now, let's add 6 to both sides to get the variable term alone.
4.5x = 26
Finally, we should divide both sides by 4.5 to get x by itself.
x = 5 7/9
Hope this helps! :)
