1) Determine the equation of QP in the form y=mx+c. 2) Determine the coordinates of Q. 3) Calulate the length OQ leave in simplest surd form. 4) Calulate the size of €. 5) If OS = √148 units, calulate the length of QS
in Geometry Answers by Level 1 User (680 points)

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

(1) QP is parallel to OS so it has the same gradient=6.

Use the point-slope form of the line equation first because the line passes through P(-3,17):

y-17=6(x+3)=6x+18, so y=6x+35 is the equation of QP.

(2) The coordinates of Q are where OQ and QP meet:

y=-x=6x+35, so 7x=-35, x=-5 and y=-x=5. So Q(-5,5).

(3) Using Pythagoras on the right triangle formed by the perpendicular from Q to the x-axis=y coordinate=5, where OQ is the hypotenuse and the other leg is the magnitude of the x coordinate=5, we have OQ=√(5²+5²)=5√2 units (=7.07 units approx).

(4) The angle between QO and the negative x-axis is 45º (arctan(5/5)=arctan(1)). The tangent of the angle between OS and the positive x-axis is 6, the slope of OS. So since QOS is between these two angles we know that they add up to 180º. QOS=180-45-arctan(6)=135-arctan(6)=54.46º approx.

(5) OS=√(12²+2²)=√148 (also given). The equation of PS is:

y-17=-(x+3), y=14-x. The coordinates of S are the solution of y=6x=14-x, 7x=14, x=2, y=6x=12, giving S(2,12), hence OS=√148. QS is the hypotenuse of a right triangle with leg lengths 2-(-5)=7 (horizontal), 12-5=7 (vertical). QS=√(7²+7²)=7√2=9.90 units approx.

by Top Rated User (1.2m points)

Related questions

1 answer
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
87,516 questions
100,344 answers
2,420 comments
764,327 users