given triangle ABC with A(-3,2), B(-1,-4), and C(4,1) write the equation for the line containing altitude LINE AR in standard form.
a. x-y=1
b. x+y=-1
c. x+y=1
d. x-y=-1
clearly, with the point (-3,2), x+y = -1
so you got to
(y - 2) = -x - 3
x+y = -3+2 = -1
Apologies for the mistake in the previous response. You are correct.
Using the point-slope form and the point (-3,2):
(y - 2) = -1(x + 3)
y - 2 = -x - 3
Rearranging the equation in standard form:
x + y = -1
Therefore, the equation for the line containing altitude LINE AR in standard form is x + y = -1.
The correct answer is b. x + y = -1.
To find the equation for the line containing altitude LINE AR, we need to find the coordinates of point R. The altitude LINE AR is perpendicular to base BC and passes through the vertex A.
First, let's find the slope of base BC. The slope formula is given by (y2 - y1) / (x2 - x1).
Taking points B(-1,-4) and C(4,1), the slope of BC is (1 - (-4)) / (4 - (-1)) = 5/5 = 1.
Since the altitude LINE AR is perpendicular to base BC, the slope of LINE AR is the negative reciprocal of 1, which is -1.
Now, we have the slope (-1) and the point A(-3,2) that the line passes through. We can use the point-slope form to write the equation of the line:
(y - y1) = m(x - x1)
Using point A(-3,2) and the slope -1:
(y - 2) = -1(x - (-3))
(y - 2) = -1(x + 3)
(y - 2) = -x - 3
Let's rearrange the equation in standard form, which is ax + by = c:
x + y = -5
Therefore, the equation for the line containing altitude LINE AR in standard form is: x + y = -5.
The answer is not given among the options provided (a. x-y=1, b. x+y=-1, c. x+y=1, d. x-y=-1).