Question

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

Answer 1

C (0, 2)

Explanation:

Answer 2

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.

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 = (-8 - 4 )/(2 -(-2)) \\\\ m_1 = (-12 )/(2+2) \\\\m_1 = (-12 )/(4) \\\\m_1 = -3 \\\\`

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

`m_2 = - (1)/(m_1)`

So the slope of the other line is

`m_2 = (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 = (1 )/(3) (x - 6)\\\\`

To get the y-intercept, substitute x = 0

`y - 4 = (1 )/(3) (0 - 6) \\\\y - 4 = (-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.