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Standard VII

Mathematics

Perpendicular Bisector

Given A̅B̅ =...

Question

Given $¯ A B = 3.9$ cm,construct $¯ P Q$ such that the length of $¯ P Q$ is twice that of $¯ A B$

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Solution

$1.$ Draw a line $l$ mark a point $P$ on it

$2.$ Measure $¯ A B = 3.9$ cm usig compass.

$3.$ Now keeping compass opened the same length.We keep pointed end at point $P,$ and draw an arc on line $l$

So, $¯ P X = 3.9$ cm

$4.$ Now keeping compass opened the same length.We keep pointed end at point $X$ and draw an arc on line $l$

So, $¯ X Q = 3.9$ cm

And $¯ P Q = 7.8$ cm

Thus, $¯ P Q$ is twice that of $¯ A B$

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are two points such that the direction cosines of

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l = \frac{x_{2} - x_{1}}{∣ ∣ ¯ A B ∣ ∣}

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Q. Given

¯ ¯¯¯¯¯¯ ¯ A B

of length 3.9 cm, construct

¯ ¯¯¯¯¯¯ ¯ P Q

such that the length

¯ ¯¯¯¯¯¯ ¯ P Q

is twice that of AB . Verify by measurement.

(Hint: Construct

¯ ¯¯¯¯¯¯¯ ¯ P X

such that length of

¯ ¯¯¯¯¯¯¯ ¯ P X

= length of

¯ ¯¯¯¯¯¯ ¯ A B

;
then cut off

¯ ¯¯¯¯¯¯¯ ¯ X Q

such that

¯ ¯¯¯¯¯¯¯ ¯ X Q

also has the length of

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Question 4

Given $¯ ¯¯¯¯¯¯ ¯ A B$ of length 3.9 cm, construct $¯ ¯¯¯¯¯¯ ¯ P Q$ such that the length $¯ ¯¯¯¯¯¯ ¯ P Q$ is twice that of AB . Verify by measurement.

(Hint: Construct $¯ ¯¯¯¯¯¯¯ ¯ P X$ such that length of $¯ ¯¯¯¯¯¯¯ ¯ P X$ = length of $¯ ¯¯¯¯¯¯ ¯ A B$ ;
then cut off $¯ ¯¯¯¯¯¯¯ ¯ X Q$ such that $¯ ¯¯¯¯¯¯¯ ¯ X Q$ also has the length of $¯ ¯¯¯¯¯¯ ¯ A B$ .)

Q. In regular hexagon

A B C D E F

, prove that

¯ A B ∥ ¯ D E

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Given¯AB=3.9cm,construct ¯PQ such that the length of ¯PQ is twice that of ¯AB

Given $¯ A B = 3.9$ cm,construct $¯ P Q$ such that the length of $¯ P Q$ is twice that of $¯ A B$