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A circle is centered at the point (-7, -1) and passes through the point (8, 7).The radius of the circle is____ units. The point

denis-greek [22]

Answer:

Part 1) The radius of the circle is r=17 units

Part 2) The points (-15,14) and (-15,-16) lies on this circle

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance between the center of the circle and any point on the circle is equal to the radius of the circle

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

(-7, -1) and (8, 7)

substitute

$r=\sqrt{(7+1)^{2}+(8+7)^{2}}$

$r=\sqrt{(8)^{2}+(15)^{2}}$

$r=\sqrt{289}$

$r=17\ units$

step 2

Find out the y-coordinate of point (-15,y)

The equation of the circle in standard form is equal to

$(x-h)^2+(y-k)^2=r^2$

where

(h,k) is the center

r is the radius

substitute the values

$(x+7)^2+(y+1)^2=17^2$

$(x+7)^2+(y+1)^2=289$

Substitute the value of x=-15 in the equation

$(-15+7)^2+(y+1)^2=289$

$64+(y+1)^2=289$

$(y+1)^2=289-64$

$(y+1)^2=225$

square root both sides

$(y+1)=(+/-)15$

$y=-1(+/-)15$

$y=-1(+)15=14$

$y=-1(-)15=-16$

therefore

we have two solutions

point (-15,14) and point (-15,-16)

see the attached figure to better understand the problem

8 0

3 years ago

Segment BD is an altitude of triangle ABC. Find the area of the triangle.

Sever21 [200]

Answer: The correct option is A, i.e., 7.5.

Explanation:

It is given that ABC is a triangle and BD is an altitude.

Since BD is an altitude, therefore the height of the triangle is BD and the base of the triangle is AC.

The distance formula to find the distance between two points is,

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

First, we find BD, where B(-1,4) and D(2,4).

$BD=\sqrt{(2+1)^2+(4-4)^2}=\sqrt{9} =3$

So, the height of the triangle is 3.

Now, we find the value of AC, where A(2,1) and C(2,6).

$AC=\sqrt{(6-1)^2+(2-2)^2}=\sqrt{25} =5$

So, the base of the triangle is 5.

The formula to find the area of a triangle is,

$A=\frac{1}{2}\times {\text{base}}\times {\text{height}}$

$A=\frac{1}{2}\times 5\times 3=\frac{15}{2}=7.5$

Therefore, the area of the triangle is 7.5 unit square and the correct option is A.

6 0

3 years ago

Read 2 more answers

Caroline drew the blueprints of her new kitchen on a coordinate plane. The coordinates of the four corners of her square kitchen

puteri [66]

Answer:

If it is a square kitchen the walls will be 12 units long

Step-by-step explanation:

To get from 2,4 into -10,4 you move down 12 units

3 0

3 years ago

Read 2 more answers

Is the sum of two monomials always a monomial? Is their product always a monomial?

Ivan

Sum of two monomials is not necessarily always a monomial.

For example:

Suppose we have two monomials as 2x and 5x.

Adding 2x+5x , we get 7x.

So if two monomials are both like terms then their sum will be a monomial.

Suppose we have two monomials as 3y and 4x

Now these are both monomials but unlike, so we cannot add them together and sum would be 3y + 4x , which is a binomial.

So if we have like terms then the sum is monomial but if we have unlike terms sum is binomial.

Product of monomials:

suppose we have 2x and 5y,

Product : 2x*5y = 10xy ( which is a monomial)

So yes product of two monomials is always a monomial.

4 0

3 years ago

Read 2 more answers

In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 7000 kilometers, what should

yan [13]

If 1mm = 500km then:

7000km/500km will give you your diameter of the drawing.

This means the planet drawing will have a diameter of 14mm

6 0

3 years ago