Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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 C A 0 0 B 1 1 C 1 5 D 6 8 class=

Sagot :

naǫ
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.
[tex]B(4, -3) \\ x_1=4 \\ y_1=-3 \\ \\ C(-4,3) \\ x_2=-4 \\ y_2=3 \\ \\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-(-3)}{-4-4}=\frac{3+3}{-8}=\frac{6}{-8}=-\frac{3}{4} \\ \\ y=-\frac{3}{4}x+b \\ (-4,3) \\ 3=-\frac{3}{4} \times (-4)+b \\ 3=3+b \\ b=0 \\ \\ y=-\frac{3}{4}x[/tex]

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.

[tex](0,0) \\ x=0 \\ y=0 \\ \Downarrow \\ 0 \stackrel{?}{=} -\frac{3}{4} \times 0 \\ 0 \stackrel{?}{=} 0 \\ 0=0 \\ \hbox{the point lies on the line} \\ \\ (1,1) \\ x=1 \\ y=1 \\ \Downarrow \\ 1 \stackrel{?}{=} -\frac{3}{4} \times 1 \\ 1 \stackrel{?}{=} -\frac{3}{4} \\ 1 \not= -\frac{3}{4} \\ \hbox{the point doesn't lie on the line}[/tex]

[tex] (1,-5) \\ x=1 \\ y=-5 \\ \Downarrow \\ -5 \stackrel{?}{=} -\frac{3}{4} \times 1 \\ -5 \stackrel{?}{=} -\frac{3}{4} \\ -5 \not= -\frac{3}{4} \\ \hbox{the point doesn't lie on the line} \\ \\ (6,-8) \\ x=6 \\ y=-8 \\ \Downarrow \\ -8 \stackrel{?}{=} -\frac{3}{4} \times 6 \\ -8 \stackrel{?}{=} -\frac{9}{2} \\ -8 \not= -\frac{9}{2} \\ \hbox{the point doesn't lie on the line}[/tex]

The answer is A.

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 =  [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Let Coordinates of X = (0,0)

So, Slope of BX is given by

[tex]\dfrac{0+3}{0-4}=\dfrac{3}{-4}[/tex]

Slope of CX is given by

[tex]\dfrac{0-3}{0+4}=\dfrac{-3}{4}[/tex]

So, Slope of BX = Slope of CX = [tex]\dfrac{-3}{4}[/tex]

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

Hence, Option 'A' is correct.

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.