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The equation of a straight line
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19 Dec 2024, 23:47
19 Dec 2024, 23:47
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The equation of a straight line $\(L\)$ is $\(2 x+4 y=0\)$. Which of the following options must be true?
Indicate all that apply
A Line $\(L\)$ contains the point $P(0,0)$ on it.
B The straight line $\(L\)$ does not pass through the points that lie in the first and third quadrants
C The straight line $\(L\)$ does not pass through the quadrant in which the point $\(P(-2,1)\)$ lies
D The $\(x\)$-coordinates and the $\(y\)$-coordinates of points lying on the line $\(L\)$ are always of opposite sign
Indicate all that apply
A Line $\(L\)$ contains the point $P(0,0)$ on it.
B The straight line $\(L\)$ does not pass through the points that lie in the first and third quadrants
C The straight line $\(L\)$ does not pass through the quadrant in which the point $\(P(-2,1)\)$ lies
D The $\(x\)$-coordinates and the $\(y\)$-coordinates of points lying on the line $\(L\)$ are always of opposite sign
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The equation of a straight line
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20 Dec 2024, 03:57
20 Dec 2024, 03:57
1
Expert Reply
The equation of straight line $\(L\)$ is $\(2 x+4 y=0\)$; we need to check from the options that which of them is true.
(A) Line $\(L\)$ contains the point $\(P(0,0)\)$ on it - which is true as $\((0,0)\)$ satisfies the equation of line $\(L\)$.
(B) The straight line $\(L\)$ does not pass through the points that lie in the first and third quadrants which is true as a line of the form $\(\mathrm{y}=-\mathrm{kx}\)$, where k is any positive real number, passes through origin and $\(2^{\text {nd \)$ and $\(4^{\text {th \)$ quadrant only.
(C) The straight line $\(L\)$ does not pass through the quadrant in which the point $\(P(-2,1)\)$ lies which is false as point $\(\mathrm{P}(-2,1)\)$ is in the $\(2^{\text {nd \)$ quadrant and line L does pass through $\(2^{\text {nd \)$ quadrant.
(D) The $\(x\)$-coordinates and the $\(y\)$-coordinates of points lying on the line $\(L\)$ are always of opposite sign - which is not true for all points as $(0,0)$ also lies on the line $\(2 x+4 y=0\)$
Hence options (A) \& (B) are correct.
(A) Line $\(L\)$ contains the point $\(P(0,0)\)$ on it - which is true as $\((0,0)\)$ satisfies the equation of line $\(L\)$.
(B) The straight line $\(L\)$ does not pass through the points that lie in the first and third quadrants which is true as a line of the form $\(\mathrm{y}=-\mathrm{kx}\)$, where k is any positive real number, passes through origin and $\(2^{\text {nd \)$ and $\(4^{\text {th \)$ quadrant only.
(C) The straight line $\(L\)$ does not pass through the quadrant in which the point $\(P(-2,1)\)$ lies which is false as point $\(\mathrm{P}(-2,1)\)$ is in the $\(2^{\text {nd \)$ quadrant and line L does pass through $\(2^{\text {nd \)$ quadrant.
(D) The $\(x\)$-coordinates and the $\(y\)$-coordinates of points lying on the line $\(L\)$ are always of opposite sign - which is not true for all points as $(0,0)$ also lies on the line $\(2 x+4 y=0\)$
Hence options (A) \& (B) are correct.
