Question

A,B,C and D are four points with coordinates (3,- 2)(-1,6)( 1,- 3) and (1,7) respectively show that line segments AB and CD bisect​

Answer 1

Answer:

Given Information,

• A = (3,-2)
• B = (-1,6)
• C = (1,-3)
• D = (1,7)

To Prove,

• Line AB bisects Line CD

Solution,

To prove that Line AB bisects Line CD, we have to prove that both lines have the same midpoint. By this we can say that after bisecting each other, both of the lines will have same ratio of bisection.

To find the midpoint of two points, the formula is:

$\boxed{\bf{Midpoint\:(x,y) = \dfrac{x_1+x_2}{2} \:,\: \dfrac{y_1+y_2}{2}}}$

Now, calculating the midpoint of line AB we get:

• x₁ = 3
• x₂ = -1
• y₁ = -2
• y₂ = 6

$\implies Midpoint = \dfrac{3-1}{2}\:,\:\dfrac{-2+6}{2}\\\\\\\implies Midpoint = \dfrac{2}{2} \:,\: \dfrac{4}{2} = (1,2)$

Hence the midpoint of line AB is (1,2).

Calculating the midpoint of line CD we get:

• x₁ = 1
• x₂ = 1
• y₁ = -3
• y₂ = 7

$\implies Midpoint = \dfrac{1+1}{2}\:,\:\dfrac{-3+7}{2}\\\\\\\implies Midpoint = \dfrac{2}{2}\:,\:\dfrac{4}{2} = (1,2)$

Hence the midpoint of line CD is also (1,2).

Since both AB and CD have the same midpoints, both lines bisect each other.

(Refer to the graph for graphical representation.)

Answer 2

Answer:

Question :-

• A,B,C and D are the four points with co-ordinates (3,-2)(-1,6)(1,-3) and (1,7) respectively. Show that the line segment AB and CD bisect.

Answer :-

• Mid-point of a line AB is (1,2)
• Mid-point of a line CD is (1,2).

• Here both of the line AB and CD have same midpoints So.Both of the line bisects each other.

Given :-

• A ,B,C,D are the four points with co- ordinates (3,-2)(-1,6)(1,-3) and (1,7)respectively.

To prove :-

• Here we should show that the line AB and CD bisects each other.

Solution :-

《1》

• Here if should find the line AB and CD are bisects each other.

$\mathcal\purple{So,}$

• Here we should use mid point formulae that is,

$(x.y) = \frac{x1 + x2}{2} , \frac{y1 + y2}{2}$

• Here first finding mid point of a line AB .

• Now lets take values first .
• Now applying all the values we get,

$mid \: point = \frac{3 - 1}{2} \: \: \frac{ - 2 + 6}{2}$

• $mid \: point = \frac{2}{2} , \: \: \frac{4}{2} = (1,2)$

$\mathcal\red{Therefore ,}$

• The mid point of line segment AB is (1,2).

《2》

• Now calculating the mid point of a line segment CD.
• Here first you should take all values first then start to apply the values we get that,

$mid \: point = \frac{1 + 1}{2}, \: \frac{ - 3 + 7}{2}$

• Now here we get values as ,

• $\: mid \: point = \frac{2}{2} , \: \frac{4}{2} = (1,2)$

$\mathcal\red{Therefore ,}$

• The mid point of a line segment CD is (1,2).

$\mathcal\purple{Verification ;-}$

• Here we get the mid point of a line segment AB , CD is same and both the line bisects each other.

Hence proved.

Hope it helps u mate .

Thank you .