In the diagram: - Point \( K(-3 ; 10) \) and \( L \) in the first quadrant, are points on the quadrilateral KIMN . - Equation of line \( M N \) is given as \( y=-\frac{1}{3} x-1 \). - MPN forms an angle \( \alpha \) with \( x \)-axis as indicated. - \( P \) is a point of intersection of line MPN with the \( x \)-axis and \( Q \) is a point of intersection of line \( L Q M \) with \( x \)-axis. 1.1. Determine the size of \( \alpha \). 1.2. Determine the equation of the line \( K L \) if \( K L \| A M \). 1.3. a) If the equation of \( K N \) is \( y=3 x+19 \), determine the coordinate of \( N \) and hence calculate the length of \( K N \). b) If it is further given that the equation of the line \( L M \) is \( x=6 \), show that (5) \( \triangle K L N \) is isosceles. (4) \( 114] \)
Added by Amahle
Close
Step 1
1. To determine the size of α, we need to find the slope of line MN. The equation of line MN is given as y = -1/3x - 1. The slope of a line is the coefficient of x in its equation. So, the slope of line MN is -1/3. The angle α is the angle formed between line MN Show more…
Show all steps
Your feedback will help us improve your experience
Jeremiah Mbaria and 69 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
In the following figure, the points A and C lies on the x - axis and y - axis respectively. The equation of line AC is 2y + x = 16. Line BX is perpendicular to line AC. (i) Find the coordinates of X. The point D is such that the quadrilateral ABCD has AC as a line of symmetry. (ii) Find the coordinates of D. (iii) Find the perimeter of ABCD. In the following figure, equation of line AC is 2y = x + 4. AB = BC and AC is perpendicular to BD. Find the coordinates of B and C. In an isosceles triangle PQR, PQ = PR. The base QR lies on the x - axis, P lies on the y - axis and 2x - 3y + 9 = 0 is the equation of PQ. Find the equation of the straight line along PR. If x + 2y = 7 and 2x + y = 8 are the equations of the lines of two diameters of a circle, find the radius of the circle if the point (0, -2) lies on the circle.
Jeremiah M.
Column-I Column-II I. The diagonals of the parallelogram (A) $\frac{5 \pi}{12}$ whose sides are $l x+m y+n=0, l x+$ $m y+n=0, m x+l y+n=0, m x+l y+$ $n^{\prime}=0$ include an angle II. The line $x+y=2$ turns about the point (B) $\frac{\pi}{12}$ on it, whose ordinate is equal to abscissa, through an angle $\theta$ in the clockwise direction so that its equation becomes $y$ $=2 x-1$. Then, the value of the angle $\theta$ is III. The larger of the two angles made with the $x$-axis of a straight line drawn (C) $\frac{\pi}{2}$ through $(1,2)$ so that it intersects $x+y$ $=4$ at a point distant $\frac{\sqrt{6}}{3}$ from $(1,2)$ is (D) $\tan ^{-1} 3$
Quadrilateral KLMN has vertices at K(2, 6), L(3, 8), M(5, 4), and N(3, 2). It is reflected across the y-axis, resulting in quadrilateral K'L'M'N'. What are the coordinates of point N'?
James K.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD