Question

Which formula should be used to find the slope of EF? A) x = -b ± b2 - 4ac 2a B) m = y2 - y1 x2 - x1 C) m = y2 + y1 x2 + x1 D) M = (x1 + x2 2 , y1 + y2 2 )

Answer 1

Option B -
`m=(y_2-y_1)/(x_2-x_1)`

Explanation:

To find : Which formula should be used to find the slope of EF?

Solution :

The slope formula of two points
`(x_1,y_1),(x_2,y_2)` is given by,

`m=(y_2-y_1)/(x_2-x_1)`

As in given options,

A)
`x=(-b\pm√(b^2-4ac))/(2a)` is the quadratic formula used to find roots.

B)
`m=(y_2-y_1)/(x_2-x_1)` is the required formula to find the slope.

C)
`m=(y_2+y_1)/(x_2+x_1)` is not any formula.

D)
`M=((x_1+x_2)/(2),(y_1+y_2)/(2))` is the mid point formula.

Therefore, Option B is correct.

Answer 2

A) The formula x = -b ± sqrt(b2 - 4ac)/2a calculates the roots of a quadratic equation.

D) The formula M = ((x1 + x2)/2, (y1 + y2)/2) calculates the mid-point of the line joining the points
`(x_(1),y_(1))` and
`(x_(2),y_(2))`.

B) The formula m = ((y2 - y1)/(x2 - x1)) calculates the slope of a line.

Hence, option B should be used to find the slope of EF.