Parallelogram abcd has the coordinates of a(-1,10) and c(5,4). find the coordinates of where diagonals ac and bd intersect

The coordinates of where diagonals ac and bd intersect at (2,7)

Step-by-step explanation:

we are given coordinates as a(-1,10) and c(5,4)

we know that diagonals of parallelogram always bisect each other

Let's assume O is the intersection point between diagonals

So, point O bisects line ac into two equal parts

So, point O is the mid-point of ac

so, we can find point O

we get

now, we can simplify it

and we get

So,

The coordinates of where diagonals ac and bd intersect at (2,7)

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)