A line passes through #(9 ,2 )# and #( 3, 5 )#. A second line passes through #( 4, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
It can be any point on the second line, for example (0,10) as explained below.
By signing up, you agree to our Terms of Service and Privacy Policy
To find a point that the second line may pass through if it is parallel to the first line, we can use the concept that parallel lines have the same slope.
The slope of the first line passing through the points (9, 2) and (3, 5) can be calculated using the formula: [ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ] [ m = \frac{{5 - 2}}{{3 - 9}} ] [ m = \frac{{3}}{{-6}} ] [ m = -\frac{1}{2} ]
Since the second line is parallel to the first line, it must have the same slope. Now, we can use the slope-intercept form of a line (y = mx + b) and substitute the slope (-1/2) and one of the given points (4, 8) to find the y-intercept (b).
[ 8 = -\frac{1}{2}(4) + b ] [ 8 = -2 + b ] [ b = 10 ]
Now we have the slope (-1/2) and the y-intercept (10). We can use this information to find another point on the second line. Let's choose another x-coordinate, say 0, and use it to find the corresponding y-coordinate.
[ y = -\frac{1}{2}(0) + 10 ] [ y = 10 ]
So, another point that the second line may pass through is (0, 10).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- Circle A has a center at #(7 ,-5 )# and a radius of #1 #. Circle B has a center at #(4 ,2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
- A line passes through #(5 ,8 )# and #(6 ,2 )#. A second line passes through #(1 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(7 ,1 )# to #(8 ,5 )# and the triangle's area is #32 #, what are the possible coordinates of the triangle's third corner?
- A line passes through #(4 ,9 )# and #(7 ,4 )#. A second line passes through #(8 ,7 )#. What is one other point that the second line may pass through if it is parallel to the first line?
- Circle A has a center at #(1 ,-4 )# and a radius of #2 #. Circle B has a center at #(9 ,3 )# and a radius of #5 #. Do the circles overlap? If not what is the smallest distance between them?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7