draw ABC with vertices A(-2,0)B(8,8),And C (4,-2)
B) draw the median from vertex A. Then,find the equationin slope y-interceptform for this median
c)draw the right bisector of BC. Then,find the equation for this right bisector
The
To draw the median from vertex A, follow these steps:
1. Plot the points A(-2, 0), B(8, 8), and C(4, -2) on a coordinate plane.
2. Use a ruler to connect points A and the midpoint of BC. Let's call this midpoint M.
To find the equation of the median in slope-intercept form, follow these steps:
1. Calculate the coordinates of point M, which is the midpoint of BC.
- The midpoint formula is: M = ((x1 + x2) / 2, (y1 + y2) / 2).
- The coordinates of B are (8, 8), and the coordinates of C are (4, -2).
- Substituting the values into the formula: M = ((8 + 4) / 2, (8 + (-2)) / 2) = (6, 3).
2. Determine the slope of the median.
- The slope formula is: slope = (y2 - y1) / (x2 - x1).
- Let's use the point A(-2, 0) and M(6, 3) to find the slope.
- Substituting the values into the formula: slope = (3 - 0) / (6 - (-2)) = 3 / 8.
3. Use the slope-intercept form of a line, y = mx + b, to find the y-intercept.
- Substitute the slope (m) and one of the coordinates of point A (x1, y1) into the equation.
- y = mx + b becomes 0 = (3/8)(-2) + b.
- Simplifying the equation: 0 = -3/4 + b.
- Solving for b: b = 3/4.
Therefore, the equation for the median from vertex A in slope-intercept form is y = (3/8)x + 3/4.
To draw the right bisector of BC, follow these steps:
1. Plot the points B(8, 8) and C(4, -2) on a coordinate plane.
2. Use a ruler to connect the midpoints of BC. Let's call this midpoint N.
To find the equation of the right bisector, follow these steps:
1. Calculate the coordinates of point N, which is the midpoint of BC.
- The midpoint formula is: N = ((x1 + x2) / 2, (y1 + y2) / 2).
- The coordinates of B are (8, 8), and the coordinates of C are (4, -2).
- Substituting the values into the formula: N = ((8 + 4) / 2, (8 + (-2)) / 2) = (6, 3).
2. Find the slope of BC.
- The slope formula is: slope = (y2 - y1) / (x2 - x1).
- Let's use the coordinates of B (8, 8) and C (4, -2) to find the slope.
- Substituting the values into the formula: slope = (-2 - 8) / (4 - 8) = -10 / -4 = 5 / 2.
3. To find the slope of the right bisector, take the negative reciprocal of the slope of BC.
- Flip the fraction and change its sign: -2/5.
4. Use the point-slope form of a line, y - y1 = m(x - x1), to find the equation of the right bisector.
- Let's choose one of the points on the line (ex. B) and use the slope (-2/5) to find the equation.
- Substituting the values into the equation: y - 8 = -2/5(x - 8).
- Simplifying the equation: y - 8 = -2/5x + 16/5.
- Move the constant term to the right side: y = -2/5x + 16/5 + 8.
- Simplifying further: y = -2/5x + 16/5 + 40/5.
- Combining the fractions: y = -2/5x + 56/5.
Therefore, the equation for the right bisector of BC in slope-intercept form is y = (-2/5)x + 56/5.
To draw the median from vertex A in triangle ABC, follow these steps:
1. Plot the points A(-2,0), B(8,8), and C(4,-2) on a coordinate plane.
2. Draw line segment AB connecting points A and B.
3. Find the midpoint M of line segment AB. To find the midpoint, use the midpoint formula:
M = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of points A and B respectively.
4. Draw a line passing through the midpoint M and the vertex C, creating a median from vertex A.
To find the equation of the median in slope-intercept form, follow these steps:
1. Determine the slope of the median. To do this, calculate the slope of the line passing through points A and M using the slope formula:
Slope (m) = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of points A and M respectively.
2. Now that you have the slope of the median, you can find the y-intercept (b) using the point-slope form of a linear equation:
y - y1 = m(x - x1), where (x1, y1) is the coordinate of point A and m is the slope of the median.
Substitute the values of x1, y1, and m into the equation and simplify to find the y-intercept.
3. Finally, write the equation of the median in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept you found in the previous step.
To draw the right bisector of line segment BC in triangle ABC, follow these steps:
1. Plot the points A(-2,0), B(8,8), and C(4,-2) on a coordinate plane.
2. Draw line segment BC connecting points B and C.
3. Find the midpoint N of line segment BC using the midpoint formula:
N = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of points B and C respectively.
4. Determine the slope of line segment BC using the slope formula:
Slope (m) = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of points B and C respectively.
5. Find the negative reciprocal of the slope of line segment BC. The negative reciprocal is obtained by taking the negative sign and flipping the fraction. Let's call this new slope as m'.
6. Use the slope-intercept form of a linear equation (y = mx + b) and the coordinates of the midpoint N to find the equation of the right bisector. Substitute the values of m', x, and y into the equation, and solve for b.
7. Finally, write the equation of the right bisector in slope-intercept form: y = m'x + b, where m' is the negative reciprocal of the slope and b is the y-intercept you found in the previous step.
The median from A goes to the midpoint of BC at (6,3)
Its slope is 3/8, so its equation is
y = 3/8 (x+2)
The bisector of BC also goes through (6,3) with slope -2/5, so its equation is
y-3 = -2/5 (x-6)