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maxonik [38]
2 years ago
13

Which point on the y-axis lies on the line that passes through point C and is perpendicular to line AB?

Mathematics
1 answer:
SCORPION-xisa [38]2 years ago
6 0

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Which point on the y-axis lies on the line that passes through point C and is perpendicular to line AB?

A. (-6, 0)

B. (0, -6)

C. (0, 2)

D. (2, 0)

The graph of the question is attached.

Answer:

The point is (x, y) = (0, 2)

The correct option is C.

Therefore, the point (0, 2) on the y-axis lies on the line that passes through point C and is perpendicular to line AB.

Step-by-step explanation:

From the given graph, the points A and B are

(x_1, y_1) = (-2, 4) \\\\(x_2, y_2) = (2,-8) \\\\

The slope of the equation is given by

m_1 = \frac{-8 - 4 }{2 -(-2)} \\\\ m_1 = \frac{-12 }{2+2} \\\\m_1 = \frac{-12 }{4} \\\\m_1 = -3 \\\\

We know that the slopes of two perpendicular lines are negative reciprocals of each other.

m_2 = - \frac{1}{m_1}

So the slope of the other line is

m_2 = \frac{1 }{3} \\\\

Now we can find the equation of the line that is perpendicular to the line AB and passes through the point C.

From the graph, the coordinates of point C are

(x_1, y_1) = (6, 4)

The point-slope form is given by,

y - y_1 = m(x -x_1)

Substitute the value of slope and the coordinates of point C

y - 4 = \frac{1 }{3} (x - 6)\\\\

To get the y-intercept, substitute x = 0  

y - 4 = \frac{1 }{3} (0 - 6) \\\\y - 4 = \frac{-6 }{3}\\\\y - 4 = -2\\\\y = 4 -2 \\\\y = 2 \\\\

So, the point is

(x, y) = (0, 2)

The correct option is C.

Therefore, the point (0, 2) on the y-axis lies on the line that passes through point C and is perpendicular to line AB.

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