The angle of inclination of a line passing through (4,5) and (a,-5) is 45°. Find the value of a.
Did you know that the slope of a line equals the tangent of the angle that the line makes with the x-axis ?
so tan45° = 1
so we know the slope of the line is 1
(-5-5)/(a-4) = 1
a - 4 = -10
a = -6
Check with a quick sketch of the situation.
To find the value of 'a', we can use the formula for the slope of a line. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the two points are (4, 5) and (a, -5).
So, the slope of the line passing through these points is:
slope = (-5 - 5) / (a - 4)
However, we also know that the line has an angle of inclination of 45°. The slope of a line is related to its angle of inclination by the tangent function:
slope = tan(angle)
In this case, the angle is 45°, so:
tan(45°) = (-5 - 5) / (a - 4)
We know that tan(45°) is equal to 1. Placing that value into the equation, we get:
1 = (-5 - 5) / (a - 4)
Now, we can solve this equation to find the value of 'a'.
Multiply both sides of the equation by (a - 4):
(a - 4) = -10
Add 4 to both sides of the equation:
a = -10 + 4
a = -6
Therefore, the value of 'a' is -6.