If the points (a, b), (c, d) and (a + c, b + d) are collinear, then Option 1: ab = cd Option 2: ac = bd Option 3: ab = bc Option 4: ad = bc

Answer: ad = bc. Solution: For three points to be collinear, they must lie on the same straight line. This means the slope between any two pairs of points must be equal. Given points: (a, b), (c, d), and (a + c, b + d) Slope from (a, b) to (a + c, b + d): Slope_1 = ((b+d) - b)/((a+c) - a) Slope_1 = d/c Slope from (c, d) to (a + c, b + d): Slope_2 = ((b+d) - d)/((a+c) - c) Slope_2 = b/a Since the points are collinear, the slopes must be equal: d/c = b/a Cross-multiplying: ad = bc Therefore, ad = bc.

Algebra

Matrices & Determinants

Medium

common

If the points (a, b), (c, d) and (a + c, b + d) are collinear, then

$ab = cd$

$ac = bd$

$ab = bc$

$ad = bc$

✅ Correct Option: 4

For three points to be collinear, they must lie on the same straight line. This means the slope between any two pairs of points must be equal.

Given points: $(a, b)$ , $(c, d)$ , and $(a + c, b + d)$

Slope from $(a, b)$ to $(a + c, b + d)$ :

$\text{Slope}_1 = \frac{(b+d) - b}{(a+c) - a}$

$\text{Slope}_1 = \frac{d}{c}$

Slope from $(c, d)$ to $(a + c, b + d)$ :

$\text{Slope}_2 = \frac{(b+d) - d}{(a+c) - c}$

$\text{Slope}_2 = \frac{b}{a}$

Since the points are collinear, the slopes must be equal:

$\frac{d}{c} = \frac{b}{a}$

Cross-multiplying:

$ad = bc$

Therefore, $ad = bc$ .

2026: 29 May Shift 2

With reference to the matrix $A=\begin{bmatrix}5&0&0\\0&5&0\\0&0&-5\end{bmatrix}$ , which of the following are TRUE ?

A. |A|=125

B. A is a scalar matrix.

C. A is a diagonal matrix.

D. |A|=-125

Choose the correct answer from the options given below:

2026: 14 May Shift 2

Consider a determinant $\Delta=\begin{vmatrix}3a & -a+b & -a+c\\ -b+a & 3b & -b+c\\ -c+a & -c+b & 3c\end{vmatrix}$ , then

Match the LIST-I with LIST-II

	LIST-I (Value of $a, b, c$ )		LIST-II (Value of $\Delta$ )
A.	$a = 0, b = 0, c = 1$	I.	$27$
B.	$a = 0, b = 1, c = 1$	II.	$0$
C.	$a = 0, b = 2, c = -1$	III.	$6$
D.	$a = 1, b = 1, c = 1$	IV.	$-6$

Choose the correct answer from the options given below:

2022: 4 Aug Shift 1

If A and B are square matrices of same order n, then identify correct statements from the statements given below:

A. $|adj\ A| = |A|^{n-1}$

B. $|A \cdot B| = |B| \cdot |A|$

C. $adj\ A' = (adj\ A)'$

D. $adj\ AB = (adj\ A) \cdot (adj\ B)$

E. $|A^n| = |A|^n$

Choose the correct answer from the options given below:

2025: 27 May Shift 1

If A and B are invertible matrices of the same order, then $(AB)^{-1}$ is equal to

2026: 18 May Shift 2

If $A = \begin{bmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{bmatrix}$ , then which of the following is/are correct ?

A. $|A| = 1$

B. $A$ is singular matrix.

C. $|adj A| = 1$

D. $|adj.(adj A)| = 1$

Choose the correct answer from the options given below:

2023: 15 June Shift 2

If $A = \begin{bmatrix} -2 & 6 \\ -5 & -1 \end{bmatrix}$ then $A^{-1}$ is :

If the points (a, b), (c, d) and (a + c, b + d) are collinear, then

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)