Determine whether the three points are the vertices of a right triangle.

Mathematics

1 answer:

solniwko [45]3 years ago

7 0

Answer:

Step-by-step explanation:

We plot the points (x,y) in the coordinate system and the points are shown in the diagram attached.

We can draw a line y = -6 connecting the RED and BLUE points. Also, we can draw a line x = 9 connecting the BLUE and GREEN points.

The intersection of these two PERPENDICULAR LINES is at the point (9, -6) (as seen --- The blue point). So, when two perpendicular lines intersect, that point is a right angle.

So, the 3 points given INDEED make a right triangle.

So, correct answer is A

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The product of two consecutive negative integers is 600. What is the value of the lesser integer?

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X ·( x + 1 ) = 600
x² + x = 600
x² + x - 600 = 0
$x_{12} = \frac{-1+/- \sqrt{1+2400} }{2}= \frac{-1+/- \sqrt{2401} }{2}= \\ =\frac{-1+/-50}{2}$
x = ( - 1 - 49 ) / 2 = - 50 : 2 = - 25
x = - 25, x + 1 = - 24
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The equation of a circle is given below. x^{2}+(y-2.25)^{2} = \dfrac{196}{169}x 2 +(y−2.25) 2 = 169 196 x, squared, plus, left

Lostsunrise [7]

Center = $(h,k) = (0,2.25)$
Radius = $r = \frac{14}{13}$

<u>Step-by-step explanation:</u>

Here we have following equation : $x^{2}+(y-2.25)^{2} = \dfrac{196}{169}$

We need to find the center & radius of this circle . Let's find out:

We know that , Equation of a circle is given by :

⇒ $(x-h)^2+(y-k)^2=r^2$ ........(1)

Here , (h,k) are the co-ordinates of center & r is the radius of circle.Collectively called as a circle with radius r and center at (h,k) . Let's frame given equation in question :

⇒ $x^{2}+(y-2.25)^{2} = \frac{196}{169}$