MCQ Quiz- Mathematics- Coordinate Geometry: Straight Lines- Test III
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A line L intersects the three sides BC, CA, AB of a triangle ABC at P,Q,R respectively. Find the value of (BP * CQ * AR) / (PC * QA * RB)
3
2
0
1
5
The equation of the base of an equilateral triangle is 3x + 4y = 9 and its vertex is given by the point (1,2). Find the length of each side of the triangle.
4/5
1/5
3/5
(4 * square_root(3)) / 15
(2 * square_root(3)) / 15
All lines represented by the equation (2 cos A + 3 sin A)x + (3 cos A - 5 sin A)y - (5 cos A - 2 sin A) = 0; pass through a fixed point which is the point of intersection of the two lines ...
2x + 3y - 15 = 0, 3x - 5y + 2 =0
2x + 3y - 5 = 0, 3x - 5y + 12 =0
2x + 3y - 5 = 0, 3x - 5y + 2 =0
2x + 3y - 25 = 0, 3x - 5y + 12 =0
The ends of the base of an isosceles triangle are (2k,0) and (0,k). The equation of one side is x = 2k. What is the equation of the base?
x + 2y = k
x + 2y = 0
x + 2y = 2k
x + 2y + 2k = 0
For the isosceles triangle in Question 4, what are the coordinates of the vertex?
(k,5k/2)
(2k,5k/2)
(2k,2k)
(5k/2,2k)
For the isosceles triangle in Question 4, what is the equation of the remaining side?
3x - 4y = 4k
3x - 4y + 4k = 0
3x - 4y - 2k = 0
3x - 4y + 2k = 0
3x - 4y + k = 0
What is the perpendicular distance of the line (x/3 + y/4 = 1) from the Origin?
12/sqrt(5)
12
5
12/5
The coordinates of the mid-points of the sides of a triangle are (3,4), (7,3) and (1,2). Is it true that the line 2x + y - 5 = 0 is a side of the triangle ?
True
False
A(3,0) and B(6,0) are two fixed points and U(v,w) is a variable point such that AU and BU meet the Y-Axis at C and D respectively and AD meets OU at V. Is it true that CV will always pass through (2,0) for any position of U on the plane ?
True
False
If the coordinates of three points. P,Q, R satisfy the relationship xy = k ^ 2, then the orthocenter of the triangle PQR will also satisfy this relationship. This statement is:
True
False
May or may not be true, depending on the value of k.
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