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Create an image of a plain white Cartesian grid. On this grid, plot a triangle with vertices labeled as G, H, I. Position of G should be at coordinates (4, -3), H at (-4, 2), and I at (2, 4). Mark these coordinates on the grid. Draw the line HI in a bold color, such as deep blue. In a contrasting color, such as bright red, highlight the perpendicular bisector of the line HI. Ensure to exclude any written text or numerical labels beyond the triangle vertices and coordinate grid labels.

Given triangle GHI with G(4, -3), H(-4, 2), and I(2, 4), find the perpendicular bisector of line HI in standard form.

Please help? Thanks

You put the final answer in y-intercept form, it asks to put it in standard form. The correct final answer would be 3x-y=0.

The perpendicular bisector would be the line that connects with the line HI at a 90 degree angle and in the mid-point. This means that we would have to find the slope of the line HI and take the opposite. The slope of HI is 1/3. This means that the slope of the perpendicular line is -3. Now we must solve for the line that crosses through the midpoint. y=mx+b we know that m=-3 and that the midpoint is at -1,3 so x=-1 and y=3. 3=(-3)-1+b. We then solve for b and find it to be 0. So the final answer is y= -3x

Ayy, 420 views

Why did the triangle go to the doctor?

Because one of its sides was feeling a bit acute!

Alright, let's find the perpendicular bisector of line HI.

First, let's find the midpoint of line HI. The midpoint formula is (x1 + x2)/2, (y1 + y2)/2. In this case, the coordinates are:

H = (-4, 2)
I = (2, 4)

So the midpoint is:
[(-4 + 2)/2, (2 + 4)/2]
[-2/2, 6/2]
[-1, 3]

Now, let's find the slope of line HI. The slope formula is (y2 - y1)/(x2 - x1). In this case, the coordinates are:

H = (-4, 2)
I = (2, 4)

So the slope is:
(4 - 2)/(2 - (-4))
2/6
1/3

Since the perpendicular bisector of a line has a negative reciprocal slope, the slope of the perpendicular bisector will be -3/1.

Now let's use the point-slope form of a line, which is y - y1 = m(x - x1). We'll use the midpoint coordinates and the negative reciprocal slope:

y - 3 = (-3)(x + 1)

Now, let's convert this equation to the standard form, Ax + By = C:

3x + y = -3

And there you have it, the equation of the perpendicular bisector of line HI in standard form is 3x + y = -3.

Doesn’t b=7

Oh wait nvm

To find the perpendicular bisector of line HI, we first need to determine the midpoint of line HI. Then, we can find the slope of line HI and find the negative reciprocal of that slope to get the perpendicular slope. Finally, using the midpoint and perpendicular slope, we can write the equation of the perpendicular bisector in standard form.

Step 1: Find the midpoint of line HI
The midpoint formula is given by:
Midpoint = (x₁ + x₂)/2, (y₁ + y₂)/2

Coordinates of H: H(-4, 2)
Coordinates of I: I(2, 4)

Midpoint X-coordinate = (-4 + 2)/2 = -1
Midpoint Y-coordinate = (2 + 4)/2 = 3

So, the midpoint of HI is M(-1, 3).

Step 2: Find the slope of line HI
The slope formula is given by:
Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Coordinates of H: H(-4, 2)
Coordinates of I: I(2, 4)

Slope of HI = (4 - 2)/(2 - (-4)) = 2/6 = 1/3

Step 3: Find the negative reciprocal of the slope
The negative reciprocal of 1/3 is -3.

Step 4: Write the equation of the perpendicular bisector in standard form
Using the midpoint M(-1, 3) and the perpendicular slope -3, we can write the equation of the perpendicular bisector in point-slope form:
(y - y₁) = m(x - x₁)

(y - 3) = -3(x - (-1))
(y - 3) = -3(x + 1)
(y - 3) = -3x - 3
3x + y = 0

So, the equation of the perpendicular bisector of HI in standard form is 3x + y = 0.