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Mrrafil [7]
3 years ago
7

The points P and Q have coordinates (-1, 6) and (9, 0) respectively.

Mathematics
1 answer:
UNO [17]3 years ago
8 0

Answer:

3y - 5x +11=0

Step-by-step explanation:

Given

P(x_1,y_1) = (-1,6)

Q(x_2,y_2) = (9,0)

Required

The equation of l

First, calculate the slope (m) of PQ

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

m = \frac{0-6}{9--1}

m = \frac{-6}{10}

m = \frac{-3}{5}

Since l is perpendicular to PQ, the slope of l is:

m_2 = -\frac{1}{m}

m_2= -\frac{1}{-3/5}

m_2 = \frac{5}{3}

Next, calculate the midpoint of PQ

M = \frac{1}{2}(x_1 + x_2,y_1+y_2)

M = \frac{1}{2}(-1+9,6+0)

M = \frac{1}{2}(8,6)

M = (4,3)

The equation of l is:

y = m(x -x_1) + y_1

y = \frac{5}{3}(x -4) +3

Multiply through by 3

3y = 5(x -4) +9

Open bracket

3y = 5x -20 +9

3y = 5x -11

Rewrite as:

3y - 5x +11=0

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