Answer:
The first coordinate of point A is 15/2.
What are perpendicular lines?
A straight line that forms a right angle (90 degrees) with another line is referred to as being perpendicular. In other words, two lines are perpendicular to one another if they connect at a right angle. The product of the slopes of two perpendicular lines is equal to -1.
Step-by-step explanation:
The given data is:
Point A (a,-4).
A line parallel to y=4x+2 has a slope equal to 4.
The equation of the line is y=4x+c. ...........................(1)
The product of the slopes of two perpendicular lines is equal to -1, another line perpendicular to this line will have a slope -1/4.
The equation of the other line is y=-1/4x+c'..............(2)
It is given that both the lines have opposite x-intercepts.
-c/4=-4c'
⇒c'=c/16
Now since it is given that both lines 1,2 passes through point A, we will substitute point A in both the line equations.
By substituting in (1) we will get:
-4=4a+c.....................(3)
By substituting in (2) we will get:
-4=-a/4+c/16..............(4)
By multiplying (4) by 14 we get:
-64=-4a+c....................(5)
By adding (3) and (5) we get:
2c=-68
c=-34
By substituting the value of c in (3) we get:
a=(34-4)/4
a=15/2
Therefore point A is (15/2, -4)
Therefore the first coordinate of point A is 15/2.
To learn more about solving line equations refer to the link below:
https://brainly.in/question/48534636
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