Advertisements
Advertisements
Question
The reflection of the point (4, −13) about the line 5x + y + 6 = 0 is
Options
(−1, −14)
(3, 4)
(0, 0)
(1, 2)
Advertisements
Solution
Let the reflection point be A(h, k)
Now, the mid point of line joining (h, k) and (4, −13) will lie on the line 5x + y + 6 = 0
\[\therefore 5\left( \frac{h + 4}{2} \right) + \frac{k - 13}{2} + 6 = 0\]
\[ \Rightarrow 5h + 20 + k - 13 + 12 = 0\]
\[ \Rightarrow 5h + k + 19 = 0 . . . . . \left( 1 \right)\]
Now, the slope of the line joining points (h, k) and (4,−13) are perpendicular to the line 5x + y + 6 = 0.
slope of the line = −5
slope of line joining by points (h, k) and (4,−13)
\[\frac{k + 13}{h - 4}\]
\[\therefore \frac{k + 13}{h - 4}\left( - 5 \right) = - 1\]
\[ \Rightarrow 5k - h + 69 = 0 . . . . . \left( 2 \right)\]
Solving (1) and (2), we get
h = −1 and k = −14
Hence, the correct answer is option (a).
APPEARS IN
RELATED QUESTIONS
Draw a quadrilateral in the Cartesian plane, whose vertices are (–4, 5), (0, 7), (5, –5) and (–4, –2). Also, find its area.
Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).
Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.
Consider the given population and year graph. Find the slope of the line AB and using it, find what will be the population in the year 2010?
Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.
Find the slope of the lines which make the following angle with the positive direction of x-axis:
\[\frac{2\pi}{3}\]
Find the slope of a line passing through the following point:
(−3, 2) and (1, 4)
State whether the two lines in each of the following are parallel, perpendicular or neither.
Through (9, 5) and (−1, 1); through (3, −5) and (8, −3)
State whether the two lines in each of the following is parallel, perpendicular or neither.
Through (3, 15) and (16, 6); through (−5, 3) and (8, 2).
Using the method of slope, show that the following points are collinear A (4, 8), B (5, 12), C (9, 28).
Using the method of slope, show that the following points are collinear A (16, − 18), B (3, −6), C (−10, 6) .
Show that the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1).
Without using Pythagoras theorem, show that the points A (0, 4), B (1, 2) and C (3, 3) are the vertices of a right angled triangle.
Without using the distance formula, show that points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.
By using the concept of slope, show that the points (−2, −1), (4, 0), (3, 3) and (−3, 2) are the vertices of a parallelogram.
Find the equation of a straight line with slope − 1/3 and y-intercept − 4.
Find the equation of the perpendicular to the line segment joining (4, 3) and (−1, 1) if it cuts off an intercept −3 from y-axis.
Find the coordinates of the orthocentre of the triangle whose vertices are (−1, 3), (2, −1) and (0, 0).
Show that the perpendicular bisectors of the sides of a triangle are concurrent.
Find the equations of the altitudes of a ∆ ABC whose vertices are A (1, 4), B (−3, 2) and C (−5, −3).
If the image of the point (2, 1) with respect to a line mirror is (5, 2), find the equation of the mirror.
The acute angle between the medians drawn from the acute angles of a right angled isosceles triangle is
The angle between the lines 2x − y + 3 = 0 and x + 2y + 3 = 0 is
The medians AD and BE of a triangle with vertices A (0, b), B (0, 0) and C (a, 0) are perpendicular to each other, if
The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y − 11 = 0 are
Find the equation to the straight line passing through the point of intersection of the lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to the line 3x – 5y + 11 = 0.
The two lines ax + by = c and a′x + b′y = c′ are perpendicular if ______.
The reflection of the point (4, – 13) about the line 5x + y + 6 = 0 is ______.
Find the equation of one of the sides of an isosceles right angled triangle whose hypotenuse is given by 3x + 4y = 4 and the opposite vertex of the hypotenuse is (2, 2).
P1, P2 are points on either of the two lines `- sqrt(3) |x|` = 2 at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P1, P2 on the bisector of the angle between the given lines.
If p is the length of perpendicular from the origin on the line `x/a + y/b` = 1 and a2, p2, b2 are in A.P, then show that a4 + b4 = 0.
The tangent of angle between the lines whose intercepts on the axes are a, – b and b, – a, respectively, is ______.
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The co-ordinates of the point A is ______.
The lines whose vector equations are `r = 2hati - 3hatj + 7hatk + lambda (2hati + phatj + 5hatk) and r = hati - 2hatj + 3hatk + µ(3hati + phatj + phatk)` are perpendicular for all values of λ and µ if p =
