alleryWhich algebraic rule sends (p, q) across the vertical line x = a?
- (p, q − 2a)
- (p − 2a, q)
- (p, 2a − q)
- (2a − p, q)
Show answer and solution
Correct answer: D. (2a − p, q)
The two abscissas have mean a, while the ordinate stays q.
ICSE Class 10 Coordinate Geometry — practice questions — page 2
Explore 77 free Coordinate Geometry questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–60 of 77.
Which algebraic rule sends (p, q) across the vertical line x = a?Read the answer and worked solution →For (p, q), reflection across y = a follows which rule?Read the answer and worked solution →Which point stays fixed under reflection in the origin?Read the answer and worked solution →Which point is fixed by BOTH x = 2 and y = −3 reflections?Read the answer and worked solution →How many common invariant points do x = 1 and x = 4 have?Read the answer and worked solution →Reflect in x = 0, then y = 0. Which single operation is equivalent?Read the answer and worked solution →Reflect in the origin, then y = 0. What single reflection results?Read the answer and worked solution →A point is reflected twice in x = 5. What is its final position?Read the answer and worked solution →Apply x = 1 followed by x = 4 reflections to (p, q). Its position is?Read the answer and worked solution →For x = 2 and y = 3 reflections, does their order affect the result?Read the answer and worked solution →Reflect (1, 2) in x = 2, then the origin. Where does it end?Read the answer and worked solution →When do reflections of (p, q) in the two coordinate axes coincide?Read the answer and worked solution →Reflections in y = 0 and the origin give the same point. What follows?Read the answer and worked solution →A point is 3 units from x = 2. How far apart are its mirror partners?Read the answer and worked solution →P and Q are reflected partners in x = 2; R lies on x = 2. Which holds?Read the answer and worked solution →P is reflected through the origin to Q. Where is the midpoint of PQ?Read the answer and worked solution →P has x + y = 7. Its reflection in y = 0 has x + y = 1. Find P.Read the answer and worked solution →Both ends of a 5-unit segment are reflected in x = 2. Its new length is?Read the answer and worked solution →Three collinear points are reflected in y = 4. What remains true?Read the answer and worked solution →Two distinct points reflect in the same mirror line. Can they coincide?Read the answer and worked solution →P divides AB internally with AP:PB=3:1. P is nearer toRead the answer and worked solution →A=(−2,1), B=(10,7), P=(2,3). What is AP:PB?Read the answer and worked solution →A=(1,2), AP:PB=2:1 and P=(5,6) internally. Find B.Read the answer and worked solution →Trisect A=(0,0) to B=(9,6). Which are the two interior points?Read the answer and worked solution →ABCD is a parallelogram; A=(1,2), B=(5,1), C=(7,6). Find D.Read the answer and worked solution →A triangle has vertices (1,2),(4,−1),C and centroid (3,3). Find C.Read the answer and worked solution →For median AD and centroid G of a triangle, AG:GD isRead the answer and worked solution →A=(1,1), centroid G=(3,5). Find the midpoint D of the opposite side.Read the answer and worked solution →What is the slope of the line x=4?Read the answer and worked solution →A line's inclination to the positive x-axis is 135°. Its slope isRead the answer and worked solution →
Worked practice questions
For (p, q), reflection across y = a follows which rule?
- (2a − p, q)
- (p, 2a − q)
- (p, q − 2a)
- (p − 2a, q)
Show answer and solution
Correct answer: B. (p, 2a − q)
Reflection in y = a keeps p unchanged and makes the ordinates sum to 2a.
Which point stays fixed under reflection in the origin?
- Every point on y = 0
- Every point with x = y
- Every point on x = 0
- Only the point (0, 0)
Show answer and solution
Correct answer: D. Only the point (0, 0)
Both coordinates equal their negatives only when both are zero.
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