How do you find the height of a triangle on a coordinate grid?
Pick 2 points to act as the endpoints of the base.
Find the equation of that line and write it in the form Ax + By + C = 0
If the third point is (a,b), then the distance from that point to your base, which is the height, would be
Dist = (aA + bB + C)/SQRT(A^2 + B^2)
Use the absolute value of that answer.
To find the height of a triangle on a coordinate grid, you can use the coordinates of the vertices of the triangle. The height of a triangle is the distance between the base and the highest point of the triangle.
Here's the step-by-step process to find the height:
1. Identify the coordinates of the two vertices that form the base of the triangle. Let's call them (x1, y1) and (x2, y2).
2. Calculate the length of the base by using the distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
3. Determine the coordinate of the third vertex of the triangle. Let's call it (x3, y3).
4. Calculate the equation of the line that contains the base by using the two given points. This equation can be in the form of y = mx + b, where m is the slope and b is the y-intercept.
5. Find the equation of the line that is perpendicular to the base and passes through the third vertex. To do this, calculate the negative reciprocal of the slope of the base line. Let's call this slope -m'.
6. Use the equation of the line in point-slope form (y - y3) = m'(x - x3) to obtain the equation of the perpendicular line.
7. Find the intersection point of the two lines. This point should be the vertex opposite to the base. To do this, solve the system of equations formed by the line equations obtained in steps 4 and 6.
8. Finally, calculate the distance between this vertex and the base by using the distance formula as mentioned in step 2.
This distance will give you the height of the triangle on the coordinate grid.