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7. Find an equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4.
2 answers:
Answer:
3x +5y = 13
Step-by-step explanation:
The equation of a perpendicular line through a given point can be obtained by swapping the x- and y-coefficients of the original line's equation, and negating one of them. The constant in the equation needs to be chosen so the equation will be true at the given point.
<h3>Form of perpendicular line</h3>Swapping the coefficients of the given equation, we have ...
3x -5y = c . . . . . for some constant c
Negating the y-coefficient gives a perpendicular line:
3x +5y = c
<h3>Particular solution</h3>We want the equation to be true for (x, y) = (-4, 5), so the constant needs to be ...
3x +5y = 3(-4) +5(5) = -12 +25 = 13
The equation of the perpendicular line is ...
3x +5y = 13
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<em>Additional comment</em>
This process works for equations given in any form. If you start with point-slope form or slope-intercept form, some manipulation of the result may be required to get to the form you want. Standard-form or general-form equations are the easiest to apply this method to.
Note that equations in <em>standard form</em> want to have a positive leading coefficient. That is why we chose to change the sign of the y-coefficient, rather than the x-coefficient.
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Answer: Angle A = 60°, angle B = 120°, angle C = 60°, angle D = 120°
Step-by-step explanation: Please refer to the attached diagram for further details.
The question has given the parallelogram ABCD as having side AB measuring 6 units, side AK measuring 3 units and line BK has been drawn perpendicular to line AD. This means line AK forms a right angle at the point where it meets line AD. From the information provided and the figure derived from that, we have right angled triangle ABK with the right angle at point K, line AB equals 6 units and line AK equals 3 units.
Using angle A as the reference angle, line AK is the opposite (side facing the reference angle), line AB is the hypotenuse (line facing the right angle) and line AK is the adjacent (side that lies between the right angle and the reference angle).
Hence, using the trigonometric ratios,
Cos A = adjacent/hypotenuse
Cos A = 3/6
Cos A = 0.5
Checking with the calculator, (that is second function of Cos 0.5)
A = 60
The opposite sides of a parallelogram are equal (that is line AD is parallel to line BC) and therefore opposite angles are equal (that is angle A is equal to angle C).
Similarly, angle B is equal to angle D. However, angles in a quadrilateral equals 360 degrees.
Therefore, angles in parallelogram ABCD is derived as;
A + B + C + D = 360
60 + B + 60 + D = 360
120 + B + D = 360
Subtract 120 from both sides of the equation
B + D = 240
Having known that angle B equals angle D, angles B and D is derived as each half of the value 240
Angle B = 240/2
Angle B = 120
and angle D = 120
Therefore, the angles are;
A = 60, B = 120, C = 60, D = 120
