FBISE, NCP & NBF-aligned resources for Classes 9–12
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Math Chapter 7 : Topic 7
Coordinate Applications
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An airplane moves from point $(2,3)$ to $(8,6)$. The straight-line distance represents:
Reasoning: Distance formula gives shortest path.
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In map reading, coordinates represent:
Reasoning: Coordinates locate exact position.
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A ship travels from $(1,2)$ to $(1,10)$. Its path is:
Reasoning: Same $x$-coordinate$⟹$vertical motion
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The midpoint between two cities gives:
Reasoning: Midpoint gives balanced location.
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In aviation, slope represents:
Reasoning: Slope indicates direction.
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Two airports lie at $(2,4)$ and $(6,4)$. The flight path is:
Reasoning: Same $y$-coordinate$⟹$horizontal path.
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Distance between two GPS points helps determine:
Reasoning: Distance gives shortest route.
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A park is located midway between $(0,0)$ and $(10,0)$. Its position is:
Reasoning: Midpoint formula$⟹ M$ $\left(\frac{x_{1} + x_{2}}{2},\frac{y_{1} + y_{2}}{2}\right)$
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Longitude and latitude form:
Reasoning: They define coordinates on Earth.
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A drone flies diagonally from $(0,0)$ to $(6,8)$. Distance traveled is:
Reasoning: $d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}=\sqrt{36+64}=10$
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Parallel roads on a map have:
Reasoning: Parallel lines have equal slopes.
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Perpendicular streets intersect at:
Reasoning: Perpendicular lines meet at $90^{o}$.
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Slope of a vertical road is:
Reasoning: $x_{1}=x_{2} ⟹$undefined slope
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Slope of a horizontal road is:
Reasoning: No vertical change.
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A construction site is equidistant from two points. It lies:
Reasoning: Equal distance implies midpoint.
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In navigation, shortest route between two points is:
Reasoning: Straight-line distance is shortest.
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If slope of road is positive, it means:
Reasoning: Positive slope rises left to right.
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A map shows two locations with same $y$-coordinate. Movement is:
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If two paths are perpendicular, their slopes:
Reasoning: Perpendicular condition.
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Distance formula in real life is used in:
Reasoning: Used in $GPS /$navigation.
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Midpoint in landscaping helps to:
Reasoning: Determines central point.
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If two points are far apart diagonally, best method is:
Reasoning: Diagonal requires full distance formula.
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A vertical tower shown on map corresponds to:
Reasoning: Vertical line$⟹ x$ constant
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Which real-life system uses coordinate geometry directly?
Reasoning: $GPS$ uses coordinates to locate positions.
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Midpoint between two locations ensures:
Reasoning: Midpoint gives balanced access.
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