What is BQD’s degree

Geometry (15) What are the properties of the incenter of a triangle?

aleksklad [387]

The incenter of a triangle is equidistant from all sides of the triangle

The incenter is the center of the biggest circle that can be drawn in the triangle, and is called incircle

The incircle will be tangent to all sides of the triangle.

Observation:
In an equilateral triangle the incenter, circumcenter, and centroid are all the same

3 0

4 years ago

Find the equation of the line passing through the given points. Express the equation in standard form.

Artyom0805 [142]

We want to write the equation of the line passing through these two points in standard form.

First, we are going to do this in slope intercept form and then change the form to standard form, which is Ax + By = C

We will use the equation y = mx + b, and since we are given two points on the line we are going to determine the slope of the line by determining the change in the y coordinates

m = y sub2 - y sub1 divided by the change in the X coordinates x sub2 – x sub1

We will start by determining the slope

(1, -6) the 1 is x sub 1 and the 6 is y sub 1

(-7, 2) the -7 is x sub 2 and the 2 is y sub 2

2 - (-6) = 8

-7 -1 = -8

so equation now is m = -1

So now again referring back to the slope intercept of the line we now know y = -1 + b. We still have to determine b and the y intercept, and we can do this by using one of the given points and substituting in the value for y and x, and then solve for b. Since these points are on the line, they must satisfy this equation. If we use the first coordinates, we would substitute 1 for x and -6 for y.

-6 = -1 times x, which is 1 + b

b = -5

construct the line equation y = mx + b where m = -1 & b = -5

In slope intercept form the equation would be y = -x - 5

Now we want to write this in standard form now. We have to deal with two things. The x and y terms have to be on the left side and A and B and C have to be integers.

The standard form of a linear equation is Ax + By=CA x + By = C . Move all terms containing variables to the left side of the equation.

Add x to both sides of the equation.

y + x = -5

Reorder y & x

x + y = -5

3 0

4 years ago

The vertex of this parabola is at (-2,-3). When the y-value is -2, the x-value is -5. What is the coefficient of the squared ter

ra1l [238]

Answer:

The coefficient of the squared term of the equation is 1/9.

Step-by-step explanation:

We are given that the vertex of the parabola is at (-2, -3). We also know that when the y-value is -2, the x-value is -5. Using this information we want to find the cofficient of the squared term in the parabola's equation.

Since we are given the vertex, we can use the vertex form:

$\displaystyle y=a(x-h)^2+k$