What is the square root of -1?

The given line segment has a midpoint at (3, 1).

Katena32 [7]

Answer:

$y=\frac{1}{3}x$

Step-by-step explanation:

The given line segment has a midpoint at (3, 1) and goes through (2, 4), (3, 1), and (4, -2). We can use any two of the three points to calculate the equation of the line. Let us use the points (2, 4) and (4, -2)

Therefore the line goes through (2, 4) and (4, -2). The equation of a line passing through $(x_1,y_1)\ and\ (x_2,y_2)$ is:

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$ .

Therefore the line passing through (2, 4) and (4, -2) has an equation:

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\\\frac{y-4}{x-2}=\frac{-2-4}{4-2}\\\frac{y-4}{x-2}=\frac{-6}{2}\\y-4=x-2(-3)\\y-4=-3x+6\\y=-3x+10$

Comparing with the general equation of line: y = mx + c, the slope (m) = -3 and the intercept on the y axis (c) = 10

Two lines are said to be perpendicular if the product of their slope is -1. If the slope of line one is m1 and the slope of line 2 = m2, then the two lines are perpendicular if:

$m_1m_2=-1$ .

Therefore The slope (m2) of the perpendicular bisector of y = -3x + 10 is:

$m_1m_2=-1\\-3m_2=-1\\m_2=\frac{1}{3}$

Since it is the perpendicular bisector of the given line segment, it passes through the midpoint (3, 1). The equation of the perpendicular bisector is:

$\frac{y-y_1}{x-x_1}=m\\\frac{y-1}{x-3}=\frac{1}{3}\\ y-1= \frac{1}{3}(x-3)\\ y-1=\frac{1}{3}x-1\\y=\frac{1}{3}x$

the equation, in slope-intercept form, of the perpendicular bisector of the given line segment is $y=\frac{1}{3}x$

7 0

3 years ago

Read 2 more answers

Suppose A and B represent mutually exclusive events.

mart [117]

Answer:

14/15

Step-by-step explanation:

simple

3/5 + 1/3= 14/15

4 0

3 years ago

Michael put the following items in his shopping basket

lesantik [10]

Answer:

c. $9

Step-by-step explanation:

$3.98 + $4.19 + $0.79 = $8.96

Round to the nearest whole number which would be 9

4 0

3 years ago

If the mesure of angle

NISA [10]

Answer:

where is the figure to denote angles??

5 0

2 years ago

Read 2 more answers

HELP Determine whether the relation is a function y=2w=2

nexus9112 [7]

Answer:

Hi there!

I might be able to help you!

It is NOT a function.

Determining whether a relation is a function on a graph is relatively easy by using the vertical line test. If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function. X = y2 would be a sideways parabola and therefore not a function. Good test for function: Vertical Line test. If a vertical line passes through two points on the graph of a relation, it is not a function. A relation which is not a function. The x-intercept of a function is calculated by substituting the value of f(x) as zero. Similarly, the y-intercept of a function is calculated by substituting the value of x as zero. The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope.

A relation that is not a function

As we can see duplication in X-values with different y-values, then this relation is not a function.

A relation that is a function

As every value of X is different and is associated with only one value of y, this relation is a function.

Step-by-step explanation:

It's up there!

God bless you!

3 0

3 years ago