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Home » Find the equations of the medians of a triangle, the coordinates of whose vertices are (-1, 6), (-3,-9) and (5, -8).
Find the equations of the medians of a triangle, the coordinates of whose vertices are (-1, 6), (-3,-9) and (5, -8).
CBSE | Class 11 | Exercise 23.5 | Maths | RD Sharma | Straight Lines
Find the equations of the medians of a triangle, the coordinates of whose vertices are (-1, 6), (-3,-9) and (5, -8).

    \[A\text{ }\left( -1,\text{ }6 \right),\text{ }B\text{ }\left( -3,\text{ }-9 \right)\text{ }and\text{ }C\text{ }\left( 5,\text{ }-8 \right)\]

be the coordinates of the given triangle.

Let:

D, E, and F be midpoints of BC, CA and AB, respectively.

hence, the coordinates of D, E and F are:

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 14

Median AD passes through

    \[A\text{ }\left( -1,\text{ }6 \right)\text{ }and\text{ }D\text{ }\left( 1,\text{ }-17/2 \right)\]

Hence on using formula,

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 15

    \[4y\text{ }\text{ }24\text{ }=\text{ }-29x\text{ }\text{ }29\]

    \[29x\text{ }+\text{ }4y\text{ }+\text{ }5\text{ }=\text{ }0\]

In the same way,

Median BE passes through

    \[B\text{ }\left( -3,-9 \right)\text{ }and\text{ }E\text{ }\left( 2,-1 \right)\]

Hence by using formula,

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 16

    \[5y\text{ }+\text{ }45\text{ }=\text{ }8x\text{ }+\text{ }24\]

    \[8x\text{ }\text{ }5y\text{ }\text{ }21=0\]

In the same way,

Median CF passes through

    \[C\text{ }\left( 5,-8 \right)\text{ }and\text{ }F\left( -2,-3/2 \right)\]

Hence on using formula,

A (−1, 6), B (−3, −9) and C (5, −8) be the coordinates of the given triangle.

Let us assume: D, E, and F be midpoints of BC, CA and AB, respectively. So, the coordinates of D, E and F are

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 14

Median AD passes through A (-1, 6) and D (1, -17/2)

So, by using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 15

4y – 24 = -29x – 29

29x + 4y + 5 = 0

Similarly, Median BE passes through B (-3,-9) and E (2,-1)

So, by using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 16

5y + 45 = 8x + 24

8x – 5y – 21=0

Similarly, Median CF passes through C (5,-8) and F(-2,-3/2)

So, by using the formula,

RD Sharma Solutions for Class 11 Maths Chapter 23 – The Straight Lines - image 17

-14y – 112 = 13x – 65

13x + 14y + 47 = 0

∴ The equation of lines are: 29x + 4y + 5 = 0, 8x – 5y – 21=0 and 13x + 14y + 47 = 0

    \[-14y\text{ }\text{ }112\text{ }=\text{ }13x\text{ }\text{ }65\]

    \[13x\text{ }+\text{ }14y\text{ }+\text{ }47\text{ }=\text{ }0\]

∴ The equation of lines are:

    \[29x\text{ }+\text{ }4y\text{ }+\text{ }5\text{ }=\text{ }0,\]

    \[8x\text{ }\text{ }5y\text{ }\text{ }21=0\]

and

    \[13x\text{ }+\text{ }14y\text{ }+\text{ }47\text{ }=\text{ }0\]

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