Question

38. What are coordinates of the point of intersection of AC and BD? (7,5) (7,7) (5,7) (5,5)​

Answer 1

Answer:

The coordinators of the point of intersection of AC BD ≈

{ 5 / 7 } , { 7 / 55 }.

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Answer 2

Given:

Coordinates of points A(7, 5) ; B(7, 7) ; C(5, 7) ; D(5, 5)

To find :

The point of intersection of line joining AC and BD.

Explanation:

• To find the point of intersection of lines, we need to first derive the equation of line. If the points $(x_{1} , y_{1} )$ and $(x_{2}, y_{2} )$ join to form a line, a basic formula for this is

                               $(y -y_{1} ) = \frac{y_{2} -y_{1} }{x_{2} -x_{1} } (x- x_{1} )$

Solution :

Step 1

Substituting the values in the equation, we get

$AC = (y - 5) = \frac{(7-5)}{(5-7)} (x-7)$

This comes as line AC that is $x+y-12 = 0$    (i)

Similarly,

BD has equation $x-y=0$    (ii)

Step 2

To find the point of intersection of AC and BD, we have to solve the equation.

From equation 2,

$x-y=0 ; or\\x=y$

substituting this in equation 1, we have

$x + (x) - 12=0 ; or\\x =6$

Therefore,

$y=6$

Final answer:

Hence the point of intersection is (6 ,6).

Although your question is incomplete, you might be referring to the question below.

What are the coordinates of the point of intersection of AC and BD? A(7 ,5) ; B(7 ,7) ; C(5 ,7) ; D(5 ,5).