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The only point where we know both coordinates is O(0,0). Let's start by plotting this point.
Additionally, we know that J(m,0) is on the x-axis because it's y-coordinate is 0. Let's mark this point as well. Since both O and M are on the same y-coordinate, the side between these points will be horizontal.
As for the third point, H(m,n), we know it's on the same x-coordinate as J(m,n). Therefore, HM will be a vertical side. Since the triangle has one vertical side and one horizontal side, this is in fact a right triangle.
To find the length of any side in a coordinate plane, we can use the Distance Formula. However, for vertical or horizontal sides, the formula is not necessary when calculating the length:
Using this, we can find OM and HM
Substitute (m,n) & (0,0)
Subtract term
By the definition of a midpoint, we know that such a point bisects each of the three sides. To find the midpoint of any side we can use the Midpoint Formula.
Side | Points | M(2x1+x2,2y1+y2) | Midpoint |
---|---|---|---|
OM | (m,0),(0,0) | M(2m+0,20+0) | M(2m,0) |
HM | (m,n),(m,0) | M(2m+m,2n+0) | M(m,2n) |
OH | (m,n),(0,0) | M(2m+0,2n+0) | M(2m,2n) |