4x-5y+2x+4+6+9y+7x+2
2 answers:
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Answer:
<h3>The option B) is correct</h3><h3>Therefore the coordinate of BStep-by-step explanation:
Given that the midpoint of segment AB is (4, 2). The coordinates of point A is (2, 7).
<h3>To Find the coordinates of point B:</h3>- Let the coordinate of A be
is (2,7) respectively
- Let the coordinate of B be
- And Let M(x,y) be the mid point of line segment AB is (4,2) respectively
- The mid-point formula is
- Now substitute the coordinates int he above formula we get
- Now equating we get
Multiply by 2 we get Multiply by 2 we get
Subtracting 2 on both
the sides Subtracting 7 on both the sides
Rewritting the above equation Rewritting the equation
Step 1: Convert to slope-intercept form to find the slope of the line.
This isn't necessary if you know all the shortcuts, it just makes your life a bit easier.
Now we want to find the equations for our new lines. It's easiest to do this in slope-intercept form, so let's start finding the slope and y-intercept.
So for the perpendicular line, the slope is going to flip and change signs, this is aka its opposite reciprocal.
And for the parallel line, it'll stay the same.
⇒ 
⇒
As for the y-intercept, just apply that slope until you get a point where x=0.
(5, 1) with a rise of 2 and a run of 1...let's work backwards to (0, b)
(5, 1), (4, -1), (3, -3), (2, -5), (1, -7), (0, -9).
(5, 1) with a rise of -1 and a run of 2...let's work backwards to (0, b)
(5, 1), (3, 0), (1, -1)...gonna have to take half a step here...(0, -1.5).
Now let's construct our equations in slope-intercept form.
And now it's time to convert to general form!
Make sure we have common denominators...check.
Multiply by the denominator...
...check.
Aaaand bring everything over!
This isn't necessary if you know all the shortcuts, it just makes your life a bit easier.
Now we want to find the equations for our new lines. It's easiest to do this in slope-intercept form, so let's start finding the slope and y-intercept.
So for the perpendicular line, the slope is going to flip and change signs, this is aka its opposite reciprocal.
And for the parallel line, it'll stay the same.
As for the y-intercept, just apply that slope until you get a point where x=0.
(5, 1) with a rise of 2 and a run of 1...let's work backwards to (0, b)
(5, 1), (4, -1), (3, -3), (2, -5), (1, -7), (0, -9).
(5, 1) with a rise of -1 and a run of 2...let's work backwards to (0, b)
(5, 1), (3, 0), (1, -1)...gonna have to take half a step here...(0, -1.5).
Now let's construct our equations in slope-intercept form.
And now it's time to convert to general form!
Make sure we have common denominators...check.
Multiply by the denominator...
...check.
Aaaand bring everything over!