Coordinate Geometry Assertion–Reason PYQs Class 10 CBSE (With Answers)

Official CBSE answer · Explanation by Team TutorVertex

Assertion: True.
For (0, 4), the x-coordinate is 0.
Hence the point lies on the y-axis.

Reason: True.
Every point on the y-axis has the form (0, y).

Link: R gives the condition used to locate (0, 4) on the y-axis, so R explains A. Answer: A.

Official CBSE answer · Explanation by Team TutorVertex

Assertion: True.
On the y-axis, x = 0.
Substituting in 3x + 2y = 4 gives 2y = 4.
Therefore y = 2 and the intersection is (0, 2).

Reason: True.
The distance from the x-axis is |y|.
For P(0, 2), this distance is |2| = 2 units.

Link: R gives a distance from an axis. It does not establish that P satisfies 3x + 2y = 4, so it does not explain A. Answer: B.

Official CBSE answer · Explanation by Team TutorVertex

Assertion: False.
Using O(0, 0), OP = √[(a − 0)² + (b − 0)²]
= √(a² + b²).
For example, P(3, 4) is 5 units from O, while 3² + 4² = 25.

Reason: True.
R states the distance formula.

Link: Applying R gives √(a² + b²), rather than the expression in A. A is false and R is true. Answer: D.

Official CBSE answer · Explanation by Team TutorVertex

Assertion: False.
The distance from the x-axis is |y|.
For (−3, 5), the distance is |5| = 5 units.

Reason: CBSE treats R as true.
The abscissa is the x-coordinate; its magnitude gives the distance from the y-axis.
For (−3, 5), that distance is |−3| = 3 units.

Link: The 3-unit distance is from the y-axis, while the x-axis distance is 5 units. A is false; CBSE treats R as true using the coordinate meaning explained above. Answer: D.

Official CBSE answer · Explanation by Team TutorVertex

Assertion: True.
The midpoint is ($\frac{\text{−4 + 4}}{\text{2}}$, $\frac{\text{3 + 3}}{\text{2}}$)
= (0, 3).

Reason: True.
A midpoint divides a segment internally in ratio 1 : 1.
Substituting this ratio in the section formula gives ($\frac{\text{x₁ + x₂}}{\text{2}}$, $\frac{\text{y₁ + y₂}}{\text{2}}$).

Link: Applying the rule in R to the given endpoints gives the point stated in A. R explains A. Answer: A.

Official CBSE answer · Explanation by Team TutorVertex

Assertion: False.
By the section formula, the point is ($\frac{\text{1(−1) + 2(1)}}{\text{1 + 2}}$, $\frac{\text{1(1) + 2(2)}}{\text{1 + 2}}$)
= ($\frac{\text{1}}{\text{3}}$, $\frac{\text{5}}{\text{3}}$).
The x-coordinate is positive, so the point in A is incorrect.

Reason: True.
R states the section formula for internal division.

Link: R gives ($\frac{\text{1}}{\text{3}}$, $\frac{\text{5}}{\text{3}}$), which differs from A in the sign of the x-coordinate. A is false and R is true. Answer: D.

Official CBSE answer · Explanation by Team TutorVertex

Assertion: True.
The two parts formed by a midpoint have equal lengths.
Their ratio is 1 : 1.

Reason: False.
Let the internal ratio be m : n.
Using the x-coordinate in the section formula, −3 = $\frac{\text{−2m − 5n}}{\text{m + n}}$.
Thus −3m − 3n = −2m − 5n.
Therefore m = 2n, giving m : n = 2 : 1.
The stated ratio 1 : 2 is incorrect.

Link: A gives the midpoint ratio correctly, but the different division described in R has ratio 2 : 1. A is true and R is false. Answer: C.

Official CBSE answer · Explanation by Team TutorVertex

Assertion: True.
The radius OA = √[(4 − 2)² + (3 − 3)²] = 2.
Since OB is also a radius, (x − 2)² + (5 − 3)² = 2².
Thus (x − 2)² + 4 = 4.
Therefore (x − 2)² = 0 and x = 2.

Reason: False.
Only diameters have the centre as their midpoint.
A chord that does not pass through the centre has a different midpoint.

Link: Equal radii and the distance formula prove A. The incorrect chord claim in R does not explain it. A is true and R is false. Answer: C.

Related: Circles: related practice

Official CBSE answer · Explanation by Team TutorVertex

Assertion: True.
Let A(2, −3), B(5, 6) and let the x-axis meet AB at P in ratio AP : PB = m : n.
Since P lies on the x-axis, its y-coordinate is 0.
By the section formula, 0 = $\frac{\text{6m − 3n}}{\text{m + n}}$.
Therefore 6m = 3n, giving m : n = 1 : 2.

Reason: True.
R states the section formula for internal division.

Link: Using R with y = 0 gives the ratio in A. R explains A. Answer: A.

Official CBSE answer · Explanation by Team TutorVertex

Assertion: True. First calculate DE from its coordinates.
By the distance formula, DE = √[(−3 − 3)² + (−3 − 5)²]
= √(36 + 64)
= 10 units.
By the midpoint theorem, DE = $\frac{\text{1}}{\text{2}}$BC.
Thus BC = 2 × 10 = 20 units.

Reason: True.
R states the midpoint theorem.

Link: R gives BC = 2DE, converting the calculated distance DE into the length stated in A. R explains A. Answer: A.

Related: Triangles: midpoint-theorem practice

Official CBSE answer · Explanation by Team TutorVertex

Assertion: True.
Let the vertices be A(−1, −6), B(2, −5), C(7, 2) and D(x, y), in that order.
The midpoint of AC is ($\frac{\text{−1 + 7}}{\text{2}}$, $\frac{\text{−6 + 2}}{\text{2}}$) = (3, −2).
By R, the midpoint of BD is also (3, −2).
Thus $\frac{\text{2 + x}}{\text{2}}$ = 3 and $\frac{\text{−5 + y}}{\text{2}}$ = −2.
Therefore x = 4 and y = 1, giving D(4, 1).

Reason: True.
The diagonals of a parallelogram have a common midpoint.

Link: Equating the diagonal midpoints using R gives the fourth vertex stated in A. R explains A. Answer: A.