The point (-3, 5) lies in which quadrant?
Correct Answer: (B) II quadrant
Step-by-step Solution:x negative, y positive ⇒ Quadrant II.
Abscissa of all points on the y-axis is:
Correct Answer: (A) 0
Step-by-step Solution:Every point on y-axis has x = 0.
The point (0, -4) lies:
Correct Answer: (B) On y-axis
Step-by-step Solution:x = 0 ⇒ lies on y-axis.
Perpendicular distance of point P(3, 4) from x-axis is:
Correct Answer: (B) 4 units
Step-by-step Solution:Distance from x-axis = |y| = 4 units.
Assertion (A): Point (2, 0) lies on the x-axis.
Reason (R): Every point on x-axis has y-coordinate zero.
Correct Answer: (A) Both (A) and (R) are true and (R) is the correct explanation of (A).
Step-by-step Solution:Both A and R are true.
Assertion (A): Point (-2, -3) lies in the III quadrant.
Reason (R): In III quadrant, both abscissa and ordinate are negative.
Correct Answer: (A) Both (A) and (R) are true and (R) is the correct explanation of (A).
Step-by-step Solution:Both A and R are true.
Write abscissa and ordinate of point P(-5, 7).
Correct Answer: Abscissa = -5, Ordinate = 7
Step-by-step Solution:In (x,y), x is abscissa (-5), y is ordinate (7).
Name point of intersection of axes and its coordinates.
Correct Answer: Origin (0, 0)
Step-by-step Solution:Intersection of axes is Origin O(0,0).
Find distance of point A(-6, 8) from origin O(0, 0).
Correct Answer: 10 units
Step-by-step Solution:d = √[36 + 64] = √100 = 10 units.
Plot A(2, 2), B(2, -2), C(-2, -2), D(-2, 2). Name figure.
Correct Answer: Square of side 4 units
Step-by-step Solution:Connecting points forms a square with side 4 units.
Write quadrant/axis for P(0,5), Q(-3,0), R(-2,-4), S(4,-1).
Correct Answer: P: y-axis, Q: x-axis, R: Q3, S: Q4
Step-by-step Solution:P on y-axis, Q on x-axis, R in Q3, S in Q4.
Three vertices of rectangle are A(2,0), B(8,0), C(8,5). Find D.
Correct Answer: D(2, 5)
Step-by-step Solution:Opposite sides equal & parallel ⇒ D(2, 5).
Find area of △ABC with vertices A(0,0), B(6,0), C(0,4).
Correct Answer: 12 sq units
Step-by-step Solution:Right triangle: Base = 6, Height = 4. Area = 1/2 × 6 × 4 = 12.
Vertices of equilateral triangle of side 2a with base on y-axis centered at origin.
Correct Answer: (0, a), (0, -a), (a√3, 0)
Step-by-step Solution:Base points on y-axis: (0, a), (0, -a). Height = a√3. Vertex = (a√3, 0).
Point on x-axis 5 units left of origin. Write coordinates & distance from y-axis.
Correct Answer: (-5, 0); 5 units
Step-by-step Solution:x = -5, y = 0. Coordinates = (-5, 0). Distance = 5 units.
Case Study Scenario: Seating grid positions: A(3,4), B(6,7) and C(9,4).
Question: Determine figure formed by A, B, C.
Correct Answer: Isosceles right triangle
Step-by-step Solution:AB = 3√2, BC = 3√2, AC = 6. Forms isosceles right triangle.
Case Study Scenario: City plan streets model.
Question: Find number of cross-streets named (4, 3).
Correct Answer: 1 cross-street
Step-by-step Solution:Coordinates uniquely identify 1 cross-street.
Points A(4,3) & B(x,5) lie on circle centre O(2,3). Find x.
Correct Answer: x = 2
Step-by-step Solution:OA² = OB² ⇒ 4 = (x-2)² + 4 ⇒ (x-2)² = 0 ⇒ x = 2.
P(-2, 3) and Q(-3, 5). Find (abscissa of P) - (abscissa of Q).
Correct Answer: 1
Step-by-step Solution:-2 - (-3) = 1.
Find area of rhombus ABCD: A(3,0), B(4,5), C(-1,4), D(-2,-1).
Correct Answer: 24 sq units
Step-by-step Solution:AC = 4√2, BD = 6√2. Area = 1/2 × 4√2 × 6√2 = 24.
