Question

☆challenge for all 《brainly☆stars 》
and
《modetors》

Solve my questions in above attachment ⬆️⤴️
$\bold{Challenge!!!:-5  }$  ​

Answer 1

$\large{\underbrace{\underline{\sf{Understanding\: the\: Question}}}}$

Here this is a question from coordinate geometry where we can to find the coordinates of the points D which lies on line EF such that EF is 4 times of DE.

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EF is 4 times of DE

So:

$\sf{DE=\dfrac{1}{4} \:of\: EF}$

It means D divide the line segment EF in the ratio of 1:4.

Let the ratio 1:4 be M1: M2.

So M1=1 and M2=4

So it is obvious that this question will be solved by applying section formula.

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Coordinates of E and F are given to be (6,4) and (14,12) respectively.

Let us name these coordinates:

⇒ X1=6

⇒ X2=14

⇒ Y1=4

⇒ Y2=12

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Now we have section formula:

$\sf{\implies\bigg[\dfrac{M1X2+M2X1}{M1+M2},\dfrac{M1Y2+M2Y1}{M1+M2}\bigg]}$

$\sf{\implies\bigg[\dfrac{1(14)+4(6)}{1+4},\dfrac{1(12)+4(4)}{1+4}\bigg]}$

$\sf{\implies\bigg[\dfrac{14+24}{5},\dfrac{12+16}{5}\bigg]}$

$\sf{\implies\bigg[\dfrac{38}{5},\dfrac{28}{5}\bigg]}$

$\sf{\implies(7.6,5.6)}$

∴ Hence the required coordinates of point D are (7.6,5.6)