A line of symmetry is a line that divides a figure into two parts such that each part is the mirror image of the other. In other words, if we flip one side of the figure over the line of symmetry, it should match up <em>exactly</em> with the other side.
Let's look at a 2 examples.
In the first image provided, notice that if we flip the left side of the figure over the right side, the two sides will not match up so this is not a line of symmetry.
In the second image, if we flip the left side of the line on to the right side, it matches up exactly so it's a line of symmetry.
To solve this problem you must apply the proccedure shown below:
1- You have that the equation of the line is:
Where is the slope and
is the y-intercept.
2- Based on the information given in the problem, the lines and
are parallel, which means that both have the same slope. Therefore, you can calculate the slope of
:
3- Use the coordinates of the point to calculate the y-intercept:
4. Solve for :
5. The equation of the line is:
The answer is:
Step 1: Assign variable for the unknown that we need to find.
Let ' x ' be the number of miles traveled by Jacob so far (His distance from starting point)
Step 2: Use the sentence given to set up an equation
Sentence 1: "His distance from his starting point was exactly 100 miles more than three times the distance remaining until the finishing point"
Total distance is 2800 miles, if his distance from the starting point is 'x', then remaining distance can be represented by 2800 - x.
Using the sentence we can write the below equation...
Distributing 3 in the right side of the equation, we get...
Adding 3x on both sides of the equation, we get...
Combine like terms in the left side of the equation, we get...
Dividing 4 on both sides of the equation, we get...
Simplifying the fraction on either side of the equation, we get...
Conclusion:
Out of the 2800 miles, Jacob travelled a distance of 2125 miles and remaining miles that he need to cover will be <u>675 miles</u>.