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COORDINATE GEOMETRY || Quantitative Aptitude || CAT 2021 || 14 October
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Question 1
The equation of the hypotenuse of an isosceles right-angled triangle is 5x + 7y = 4 and the opposite vertex is the point (2, 2). Find the equations to the sides of the isosceles right-angled triangle
Question 2
If the points A(2, 3), B(5, k), and C(6, 7) are collinear, then k = ?
Question 3
The vertices of a triangle are A(3,8), B(-4,2) and C(5,-1). The area of 
is
is Question 4
The area of the triangle formed by the straight line 5x + 3y = 15 and the co-ordinate axes is:
Question 5
The graph of the equations 5x - 2y + 1 = 0 and 4y – 3x + 5 = 0, intersect at the point P(α, β). What is the value of (2α – 3β)?
Question 6
The co-ordinates of the centroid of a triangle ABC are (-1, -2). What are the co-ordinates of vertex C, if co-ordinates of A and B are (6, -4) and (-2, 2) respectively?
Question 7
The equations of the sides of a triangle are x+y-5 =0, x-y+1 =0 and y-1 =0. Then, the coordinates of the circumcenter are
Question 8
Find the area of quadrilateral ABCD. AC and BD are diagonals i.e. y-axis and x-axis respectively. The equation of line AB is 5x+4y = -40 & equation of line CD is 8x + 15y = 120. Find the area of quadrilateral ABCD.
Question 9
The equation of the line passing through the point of intersection of the lines 2x - 5y = 3, 4x - 3y + 5 = 0 and parallel to the line 2x - 3y + 5 = 0 is:
Question 10
ABCD is a parallelogram. Co-ordinates of A, B and C are (5,0), (-2,3) and (-1,4) respectively. What will be the equation of line AD?
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