given ab and its midpoint m. the coordinates of a are (-10,-3) and the coordinates of M are (-4,-1)
a. find the coordinates of B.
b. find the slope of am. c. find the slope that is perpendicular
d. find the slope that is parallel
e . write the equation of AM
answers. please check?
a.
b. slope of am is 1/3
c. -3
d. 1/3
e. y=1/3x+b
plug in (-4,-1)
-1=1/3x+-4
x=9?
so y=1/3x+9?
let B(x,y) be the other point
we know how to get the midpoint
(x - 10)/2 = -4
x-10 = -8
x = 2
(y+3)/2 = -1
y+3 = -2
y = -5
coordinates of B are (2,-5)
b) since the slope should be the same for BM , AB, and AM
I will use the original values
slope BM = -4/6 = -2/3
(you will get the same answer for the others, don't know how you got 1/3)
c) the slope of the perp. must be +3/2
d) slope of parallel is -2/3
e) since you slope is wrong, your answer is obviously wrong
y = (-2/3)x + b
(-4,-1) on it
-1 = (-2/3)(-4) + b
-1 = 8/3 + b
b = -11/3
y = (-2/3)x - 11/3
BTW , you subbed the -4 in for the b instead of the x in your solution.
a. To find the coordinates of point B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (M) of a line segment with endpoints (x1, y1) and (x2, y2) are given by the coordinates of the midpoint (m), which in this case is (-4, -1), using the formula:
xm = (x1 + x2) / 2
ym = (y1 + y2) / 2
Given that the coordinates of point A are (-10, -3), we can substitute those values into the midpoint formula:
xm = (-10 + x2) / 2, which simplifies to -4 = (-10 + x2) / 2.
Multiply both sides of the equation by 2 to get rid of the denominator:
-8 = -10 + x2.
Simplify further:
x2 = -8 + 10 = 2.
Similarly, for the y-coordinate:
ym = (-3 + y2) / 2, which simplifies to -1 = (-3 + y2) / 2.
Multiply both sides of the equation by 2 to get rid of the denominator:
-2 = -3 + y2.
Simplify further:
y2 = -2 + 3 = 1.
Therefore, the coordinates of point B are (2, 1).
b. To find the slope of line AM, we can use the slope formula. The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Given that the coordinates of points A and M are (-10, -3) and (-4, -1) respectively, we can substitute these values into the slope formula:
m = (-1 - (-3)) / (-4 - (-10))
Simplify:
m = 2 / 6
m = 1/3
Therefore, the slope of line AM is 1/3.
c. To find the slope that is perpendicular to AM, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of 1/3 is -3.
Therefore, the slope that is perpendicular to line AM is -3.
d. To find the slope that is parallel to line AM, we can use the fact that parallel lines have the same slope. The slope of line AM is 1/3, so the slope parallel to AM is also 1/3.
Therefore, the slope that is parallel to line AM is 1/3.
e. To write the equation of line AM, we can use the slope-intercept form of a line equation: y = mx + b, where m is the slope and b is the y-intercept.
From earlier, we found that the slope of line AM is 1/3. To find b, we can substitute the coordinates of point M (-4, -1) into the equation:
-1 = (1/3)(-4) + b
-1 = -4/3 + b
b = -1 + 4/3
b = 1/3.
Therefore, the equation of line AM is y = (1/3)x + (1/3).