This question tests understanding of how to find vector components by subtracting the coordinates of the initial point from the coordinates of the terminal point. A directed line segment from point M to point N represents a vector whose components are the differences in coordinates: ⟨final x - initial x, final y - initial y⟩. Using the formula for components, we substitute the given coordinates: ⟨x₂ - x₁, y₂ - y₁⟩ = ⟨2 - 2, -4 - 2⟩ = ⟨0, -6⟩. Choice B is correct because it properly subtracts the initial point coordinates from the terminal point coordinates: ⟨2 - 2, -4 - 2⟩ = ⟨0, -6⟩. Choice A reverses the subtraction order, calculating ⟨x₁ - x₂, y₁ - y₂⟩, which gives the opposite vector (same magnitude, opposite direction). The horizontal component 0 tells us the vector moves 0 units left/right, and the vertical component -6 tells us it moves 6 units down. Key to finding vector components: always subtract initial point from terminal point (terminal - initial), and remember that the first component is the change in x, the second is the change in y.

This question tests understanding of how to find vector components by subtracting the coordinates of the initial point from the coordinates of the terminal point. The component form of a vector from point A(x₁, y₁) to point B(x₂, y₂) is found by subtracting the initial point's coordinates from the terminal point's coordinates: ⟨x₂ - x₁, y₂ - y₁⟩. For a vector from A(3, -1) to B(-2, -6), we calculate the horizontal component as -2 - 3 = -5, and the vertical component as -6 - (-1) = -5, giving us the component form ⟨-5, -5⟩. Choice C is correct because it properly subtracts the initial point coordinates from the terminal point coordinates: ⟨-2 - 3, -6 - (-1)⟩ = ⟨-5, -5⟩. Choice D reverses the subtraction order, calculating ⟨x₁ - x₂, y₁ - y₂⟩, which gives the opposite vector (same magnitude, opposite direction). To avoid errors, clearly label which point is initial and which is terminal, then methodically compute x₂ - x₁ for the horizontal component and y₂ - y₁ for the vertical component. The negative sign in a component is meaningful: negative horizontal component means leftward motion, negative vertical component means downward motion.

This question tests understanding of how to find vector components by subtracting the coordinates of the initial point from the coordinates of the terminal point. To find vector components, calculate the change in x (horizontal displacement) and the change in y (vertical displacement) by subtracting initial from terminal: horizontal component = x₂ - x₁, vertical component = y₂ - y₁. For a vector from P(5, 0) to Q(-1, 3), we calculate the horizontal component as -1 - 5 = -6, and the vertical component as 3 - 0 = 3, giving us the component form ⟨-6, 3⟩. Choice B is correct because it properly subtracts the initial point coordinates from the terminal point coordinates: ⟨-1 - 5, 3 - 0⟩ = ⟨-6, 3⟩. Choice C reverses the subtraction order, calculating ⟨x₁ - x₂, y₁ - y₂⟩, which gives the opposite vector (same magnitude, opposite direction). Key to finding vector components: always subtract initial point from terminal point (terminal - initial), and remember that the first component is the change in x, the second is the change in y. The negative sign in a component is meaningful: negative horizontal component means leftward motion, negative vertical component means downward motion.

This question tests understanding of how to find vector components by subtracting the coordinates of the initial point from the coordinates of the terminal point. To find vector components, calculate the change in x (horizontal displacement) and the change in y (vertical displacement) by subtracting initial from terminal: horizontal component = x₂ - x₁, vertical component = y₂ - y₁. For a vector from A(6, -2) to B(1, 3), we calculate the horizontal component as 1 - 6 = -5, and the vertical component as 3 - (-2) = 5, giving us the component form ⟨-5, 5⟩. Choice B is correct because it properly subtracts the initial point coordinates from the terminal point coordinates: ⟨1 - 6, 3 - (-2)⟩ = ⟨-5, 5⟩. Choice A reverses the subtraction order, calculating ⟨x₁ - x₂, y₁ - y₂⟩, which gives the opposite vector (same magnitude, opposite direction). The negative sign in a component is meaningful: negative horizontal component means leftward motion, negative vertical component means downward motion. Remember that vector components are not the same as point coordinates—components represent displacement (change in position), while coordinates represent location.

This question tests understanding of how to find vector components by subtracting the coordinates of the initial point from the coordinates of the terminal point. A directed line segment from point A to point B represents a vector whose components are the differences in coordinates: ⟨final x - initial x, final y - initial y⟩. The horizontal component 3 - (-4) = 7 tells us the vector moves 7 units right, and the vertical component 5 - 0 = 5 tells us it moves 5 units up. Choice A is correct because it properly subtracts the initial point coordinates from the terminal point coordinates: ⟨3 - (-4), 5 - 0⟩ = ⟨7, 5⟩. Choice B reverses the subtraction order, calculating ⟨x₁ - x₂, y₁ - y₂⟩, which gives the opposite vector (same magnitude, opposite direction). Key to finding vector components: always subtract initial point from terminal point (terminal - initial), and remember that the first component is the change in x, the second is the change in y. To avoid errors, clearly label which point is initial and which is terminal, then methodically compute x₂ - x₁ for the horizontal component and y₂ - y₁ for the vertical component.

This question tests understanding of how to find vector components by subtracting the coordinates of the initial point from the coordinates of the terminal point. To find vector components, calculate the change in x (horizontal displacement) and the change in y (vertical displacement) by subtracting initial from terminal: horizontal component = x₂ - x₁, vertical component = y₂ - y₁. For a vector from M(7, -1) to N(2, 4), we calculate the horizontal component as 2 - 7 = -5, and the vertical component as 4 - (-1) = 5, giving us the component form ⟨-5, 5⟩. Choice A is correct because it properly subtracts the initial point coordinates from the terminal point coordinates: ⟨2 - 7, 4 - (-1)⟩ = ⟨-5, 5⟩. Choice B reverses the subtraction order, calculating ⟨x₁ - x₂, y₁ - y₂⟩, which gives the opposite vector (same magnitude, opposite direction). Check your work by visualizing: if point B is to the right of point A, the horizontal component should be positive; if B is above A, the vertical component should be positive. Key to finding vector components: always subtract initial point from terminal point (terminal - initial), and remember that the first component is the change in x, the second is the change in y.

This question tests understanding of how to find vector components by subtracting the coordinates of the initial point from the coordinates of the terminal point. The component form of a vector from point A(x₁, y₁) to point B(x₂, y₂) is found by subtracting the initial point's coordinates from the terminal point's coordinates: ⟨x₂ - x₁, y₂ - y₁⟩. For a vector from A(5, -1) to B(0, -6), we calculate the horizontal component as 0 - 5 = -5, and the vertical component as -6 - (-1) = -5, giving us the component form ⟨-5, -5⟩. Choice B is correct because it properly subtracts the initial point coordinates from the terminal point coordinates: ⟨0 - 5, -6 - (-1)⟩ = ⟨-5, -5⟩. Choice A reverses the subtraction order, calculating ⟨x₁ - x₂, y₁ - y₂⟩, which gives the opposite vector (same magnitude, opposite direction). To avoid errors, clearly label which point is initial and which is terminal, then methodically compute x₂ - x₁ for the horizontal component and y₂ - y₁ for the vertical component. The negative sign in a component is meaningful: negative horizontal component means leftward motion, negative vertical component means downward motion.

This question tests understanding of how to find vector components by subtracting the coordinates of the initial point from the coordinates of the terminal point. The component form of a vector from point A(x₁, y₁) to point B(x₂, y₂) is found by subtracting the initial point's coordinates from the terminal point's coordinates: ⟨x₂ - x₁, y₂ - y₁⟩. For a vector from (6, 1) to (2, 7), we calculate the horizontal component as 2 - 6 = -4, and the vertical component as 7 - 1 = 6, giving us the component form ⟨-4, 6⟩. Choice B is correct because it properly subtracts the initial point coordinates from the terminal point coordinates: ⟨2 - 6, 7 - 1⟩ = ⟨-4, 6⟩. Choice C adds the coordinates instead of subtracting them, which doesn't represent any meaningful vector operation for finding components. To avoid errors, clearly label which point is initial and which is terminal, then methodically compute x₂ - x₁ for the horizontal component and y₂ - y₁ for the vertical component. The negative sign in a component is meaningful: negative horizontal component means leftward motion, negative vertical component means downward motion.

This question tests understanding of how to find vector components by subtracting the coordinates of the initial point from the coordinates of the terminal point. A directed line segment from point A to point B represents a vector whose components are the differences in coordinates: ⟨final x - initial x, final y - initial y⟩. The horizontal component 5 - 0 = 5 tells us the vector moves 5 units right, and the vertical component 3 - 3 = 0 tells us it moves 0 units up or down. Choice A is correct because it properly subtracts the initial point coordinates from the terminal point coordinates: ⟨5 - 0, 3 - 3⟩ = ⟨5, 0⟩. Choice B reverses the subtraction order, calculating ⟨x₁ - x₂, y₁ - y₂⟩, which gives the opposite vector (same magnitude, opposite direction). Key to finding vector components: always subtract initial point from terminal point (terminal - initial), and remember that the first component is the change in x, the second is the change in y. Check your work by visualizing: if point B is to the right of point A, the horizontal component should be positive; if B is above A, the vertical component should be positive.

This question tests understanding of how to find vector components by subtracting the coordinates of the initial point from the coordinates of the terminal point. To find vector components, calculate the change in x (horizontal displacement) and the change in y (vertical displacement) by subtracting initial from terminal: horizontal component = x₂ - x₁, vertical component = y₂ - y₁. The horizontal component -3 - 2 = -5 tells us the vector moves 5 units left, and the vertical component 1 - 6 = -5 tells us it moves 5 units down. Choice A is correct because it properly subtracts the initial point coordinates from the terminal point coordinates: ⟨-3 - 2, 1 - 6⟩ = ⟨-5, -5⟩. Choice B reverses the subtraction order, calculating ⟨x₁ - x₂, y₁ - y₂⟩, which gives the opposite vector (same magnitude, opposite direction). Remember that vector components are not the same as point coordinates—components represent displacement (change in position), while coordinates represent location. The negative sign in a component is meaningful: negative horizontal component means leftward motion, negative vertical component means downward motion.