MATHEMATICS MIDDLE SCHOOL

Please help!Which point is collinear with points B and C?



A.
(0, 0)

B.
(1, 1)

C.
(1, –5)

D.
(6, –8)
please help! Which point is collinear with points B and - 1

Answers

Answer 1
Answer:

Answer:  Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Coordinates of B = (4,-3)

Coordinates of C = (-4,3)

We need to find the collinear  point with B and C.

There is one method to find the collinear point i.e. Slope method.

Slope of BX = Slope of CX =  (y_2-y_1)/(x_2-x_1)

Let Coordinates of X = (0,0)

So, Slope of BX is given by

(0+3)/(0-4)=(3)/(-4)

Slope of CX is given by

(0-3)/(0+4)=(-3)/(4)

So, Slope of BX = Slope of CX = (-3)/(4)

And we can see from the graph (0,0) is the collinear point with B and C too.

Hence, Option 'A' is correct.
Answer 2
Answer: Points are collinear if they lie on the same line.

First find the equation of the line that passes through the points B and C.
B(4, -3) \nx_1=4 \n y_1=-3 \n \nC(-4,3) \nx_2=-4 \n y_2=3 \n \nm=(y_2-y_1)/(x_2-x_1)=(3-(-3))/(-4-4)=(3+3)/(-8)=(6)/(-8)=-(3)/(4) \n \ny=-(3)/(4)x+b \n(-4,3) \n3=-(3)/(4) * (-4)+b \n3=3+b \nb=0 \n \ny=-(3)/(4)x

The points lie on the line y=(-3/4)x.
Now plug the coordinates of the given points into the equation and check if they satisfy the equation.

(0,0) \nx=0 \n y=0 \n \Downarrow \n0 \stackrel{?}{=} -(3)/(4) * 0 \n0 \stackrel{?}{=} 0 \n0=0 \n\hbox{the point lies on the line} \n \n(1,1) \nx=1 \n y=1 \n \Downarrow \n1 \stackrel{?}{=} -(3)/(4) * 1 \n1 \stackrel{?}{=} -(3)/(4) \n1 \not= -(3)/(4) \n\hbox{the point doesn't lie on the line}

(1,-5) \nx=1 \n y=-5 \n \Downarrow \n -5 \stackrel{?}{=} -(3)/(4) * 1 \n-5 \stackrel{?}{=} -(3)/(4) \n-5 \not= -(3)/(4) \n\hbox{the point doesn't lie on the line} \n \n(6,-8) \nx=6 \n y=-8 \n \Downarrow \n-8 \stackrel{?}{=} -(3)/(4) * 6 \n-8 \stackrel{?}{=} -(9)/(2) \n-8 \not= -(9)/(2) \n\hbox{the point doesn't lie on the line}

The answer is A.

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Thank you!

Answers

Answer:

A = 4 * 2 1/2

A = 4*5/2

Step-by-step explanation:

A = l*w

A = 4 * 2 1/2

Another way to write 2 1/2 is as an improper fraction

A = 4 * (2*2+1)/5

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Oranges cost $1.79 a pound. Miguel bought 3.6 pounds of oranges. How much did the oranges cost, to the nearest cent?

Answers

Answer: 644cents

Step-by-step explanation:

From the question, we were told that

1 pound = $1.79

Miguel bought 3.6 pounds of oranges. This will cost

$1.79 x 3.6 = $6.444

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Write the equation of a vertical ellipse with a major axis of 20, a minor axis of 12, and a center of (6, 3)

Answers

Answer:

The equation of a vertical ellipse is  ((x-6)^2)/(100) + ((y-3)^2)/(36)   = 1\n

Step-by-step explanation:

Here, given:

Length of major axis:  20

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Length of minor axis:  12

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Also, center (h,k)  = (6,3)

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((x-h)^2)/(a^2) + ((y-k)^2)/(b^2)   = 1\n

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