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PQR is a triangle with vertices P(-2, 4), Q(4, 0) and R(3, 6) - Scottish Highers Maths - Question 1 - 2018

Question 1

PQR is a triangle with vertices P(-2, 4), Q(4, 0) and R(3, 6). Find the equation of the median through R.

Worked Solution & Example Answer:PQR is a triangle with vertices P(-2, 4), Q(4, 0) and R(3, 6) - Scottish Highers Maths - Question 1 - 2018

Step 1

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Answer

To find the mid-point M of line segment PQ, we use the mid-point formula:

$M_{PQ} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$

Here, P(-2, 4) and Q(4, 0).

Calculating the coordinates:

$M_{PQ} = \left( \frac{-2 + 4}{2}, \frac{4 + 0}{2} \right) = \left( 1, 2 \right)$

Step 2

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Answer

The gradient (slope) of the median RM can be calculated using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting R(3, 6) and M(1, 2):

$m_{RM} = \frac{2 - 6}{1 - 3} = \frac{-4}{-2} = 2$

Step 3

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Answer

To find the equation of the line for the median RM, we use the point-slope form of the equation:

$y - y_1 = m(x - x_1)$

Using point R(3, 6) and gradient 2:

$y - 6 = 2(x - 3)$

Expanding this equation gives:

$y - 6 = 2x - 6$

Therefore, the equation simplifies to:

$y = 2x$

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