Gerry thinks that the points (4,2) and (−1,4) form a line perpendicular to a line with slope 4. Do you agree? Why
1 answer:
Answer:
The answer to your question is these lines are not perpendicular.
Step-by-step explanation:
Data
A (4, 2)
B (-1, 4)
slope = m = 4
Perpendicular lines mean that these lines cross and form an angle of 90°. Also, the slope of perpendicular lines is negative reciprocals.
Process
1.- Find the slope of the second line and compare it to the slope given.
slope =
Substitution
slope =
Simplification and result
slope =
-2/5 is not a negative reciprocal of 4, so these lines are not perpendicular.
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Answer:
2nd option
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
the centre is at the midpoint of the endpoints of the diameter.
The coordinates of the centre is the average of the coordinates of the endpoints.
centre = ( ,
) = (
,
) = (- 1, 3 )
the radius is the distance from the centre to either of the endpoints
using the distance formula to calculate r
r =
with (x₁, y₁ ) = (- 1, 3 ) and (x₂, y₂ ) = (2, - 1 )
r =
=
=
=
=
= 5
then equation of circle is
(x - (- 1) )² + (y - 3)² = 5² , that is
(x + 1)² + (y - 3)² = 25