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D, E and F are the mid-points of sides o...

D, E and F are the mid-points of sides of `Delta ABC`. P, Q, R are the mid-points of sides DEF. This process of marking the mid-points and forming a new triangle is continued. How are the areas of these triangles related?

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The correct Answer is:
`1 : 4`
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Find the mid - point of side BC of DeltaABC with A(1,-4) and the mid - points of the sides through A being (2,-1) and (0,1)

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Knowledge Check

  • In Delta ABC , D and E are the mid-points of AB and AC respectively, then the area of Delta ADE is :

    A
    `4 Delta ABC`
    B
    `1/4 Delta ABC`
    C
    `2 Delta ABC`
    D
    `1/2 Delta ABC`

  • If D is the mid-point of side BC of a triangle ABC and AD is perpendicular to AC, then

    A
    `a^(2)+b^(2)=5c^(2)`
    B
    `3a^(2)=b^(2)-3c^(2)`
    C
    `b^(2)=a^(2)-c^(2)`
    D
    `3b^(2)=a^(2)-c^(2)`

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