FBISE, NCP & NBF-aligned resources for Classes 9–12
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Math Chapter 7 : Topic 2
The distance formula is derived using
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The midpoint of a line segment represents:
Reasoning: Midpoint is obtained by averaging $x$ and $y$ coordinates of endpoints.
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Find the midpoint of $A(2,4)$ and $B(6,8)$.
Reasoning: $M$ $\left(\frac{x_{1} + x_{2}}{2},\frac{y_{1} + y_{2}}{2}\right)=\left(\frac{2 + 6}{2},\frac{4 + 8}{2}\right)$ $=\left(4,6\right)$
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If one endpoint is $(0,0)$ and the other is $(8,6)$, the midpoint is:
Reasoning: Average of coordinates$⟹ (4,3)$
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If midpoint of $(x,2)$ and $(4,6)$ is $(3,4)$, then $x$ equals:
Reasoning: $\frac{x + 4}{2}$ $=3 ⟹ x=2$
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Which property is always true for the midpoint?
Reasoning: Midpoint always divides the segment equally.
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Midpoint of $(- 2, 4)$ and $(6, - 2)$ is:
Reasoning: $\left(\frac{4}{2},\frac{2}{2}\right)$ $=\left(2,1\right)$
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If midpoint is $(0,0)$, then endpoints must be:
Reasoning: Coordinates cancel each other out $(x$ and $- x)$.
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Midpoint of $(3,5)$ and $(7,5)$ lies on:
Reasoning: Same $y$-coordinate$⟹$horizontal line
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Which expression gives $x$-coordinate of midpoint?
Reasoning: Average of $x$-coordinates.
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Midpoint of $(- 4, - 6)$ and $(4, 6)$ is:
Reasoning: Symmetry cancels values.
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If midpoint is $(5,3)$ and one endpoint is $(2,1)$, the other endpoint is:
Reasoning: $\frac{2 + x}{2}$ $=5 ⟹ x=8$ ; $\frac{1 + y}{2}$ $=3 ⟹ y=5$
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Which situation gives midpoint equal to one endpoint?
Reasoning: If endpoints are identical, midpoint is same point.
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Midpoint of $(a,b)$ and $(c,d)$ depends on:
Reasoning: It uses averaging of coordinates.
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If endpoints are $(1,3)$ and $(5,7)$, midpoint is:
Reasoning: $(6/2,10/2)=(3,5)$
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Midpoint formula is derived from:
Reasoning: Midpoint is special case of section formula.
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If midpoint is $(2, - 3)$, endpoints could be:
Reasoning: All satisfy midpoint condition.
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Midpoint always lies:
Reasoning: It is central point of segment.
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If endpoints have same $x$-coordinate, midpoint lies:
Reasoning: $x$ remains constant.
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Midpoint of $(2a, 2b)$ and $(4a, 4b)$ is:
Reasoning: Average gives $(3a,3b)$.
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If midpoint is $(m,n)$, then:
Reasoning: Coordinates are averages.
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Midpoint divides a segment into:
Reasoning: By definition, midpoint divides equally.
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Midpoint of $(0,6)$ and $(6,0)$ is:
Reasoning: Average coordinates$⟹ (3,3)$
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If endpoints are reflections across origin, midpoint is:
Reasoning: Opposite coordinates cancel.
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Midpoint helps in finding:
Reasoning: It gives central point.
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