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Which point is negative five, negative six on the coordinate plane 𝑂; 𝐼, 𝐽?
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We begin by noting that the six points 𝐴 through 𝐹 lie in an orthonormal coordinate plane.
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We know this since the 𝑥- and 𝑦-axes are perpendicular and the unit lengths 𝑂𝐼 and 𝑂𝐽 in the 𝑥- and 𝑦-direction, respectively, are equal.
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We can see from the figure that one square represents one unit.
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As we are trying to identify the point with coordinates negative five, negative six, we need to move five units in the negative 𝑥-direction and six units in the negative 𝑦-direction from the origin 𝑂.
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Since both the 𝑥- and 𝑦-coordinates are negative, our point must lie in the third quadrant.
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This suggests that the correct answer must be point 𝐹.
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We can check this by marking on negative five on the 𝑥-axis and negative six on the 𝑦-axis.
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We can then draw a line parallel to the 𝑦-axis that intersects the 𝑥-axis at negative five and a line parallel to the 𝑥-axis that intersects the 𝑦-axis at negative six.
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As these lines intersect at point 𝐹, we can conclude that the point 𝐹 has coordinates negative five, negative six on the coordinate plane 𝑂; 𝐼, 𝐽.