A right triangle is drawn on a coordinate plane. Its base is the line segment between
(2, 2)
and
(9, 2).
The hypotenuse is a line segment that begins at
(2, 2)
and has slope 1.25. Find the coordinates of the third point.
a slope of 1.25 means that y changes 1.25 as fast as x.
The base of the triangle is 7 units long, so the height is 7*1.25 = 8.75 units.
(2,2)+(7,8.75) = (9,10.75)
To find the coordinates of the third point of the right triangle, we need to find the coordinates of the endpoint of the hypotenuse.
First, let's find the equation of the hypotenuse line.
We know that the starting point of the hypotenuse is (2, 2), and the slope is 1.25. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the given values, we have the equation:
y = 1.25x + b
Now, we need to find the value of b. We can substitute the coordinates of the starting point (2, 2) into the equation and solve for b.
2 = 1.25(2) + b
2 = 2.5 + b
b = 2 - 2.5
b = -0.5
Now that we have the equation of the hypotenuse line, y = 1.25x - 0.5, we can find the coordinates of the endpoint.
To find the x-coordinate, we can set y = 0 because the hypotenuse line crosses the x-axis at some point.
0 = 1.25x - 0.5
1.25x = 0.5
x = 0.5 / 1.25
x = 0.4
Therefore, the x-coordinate of the endpoint is 0.4.
We can substitute the x-coordinate into the equation of the hypotenuse to find the y-coordinate.
y = 1.25(0.4) - 0.5
y = 0.5 - 0.5
y = 0
Therefore, the y-coordinate of the endpoint is 0.
So, the coordinates of the third point of the right triangle are (0.4, 0).
To find the coordinates of the third point of the right triangle, we need to determine the height of the triangle.
First, let's calculate the length of the base of the right triangle using the coordinates (2, 2) and (9, 2). The length of the base is equal to the difference in the x-coordinates, which is:
Length_base = 9 - 2 = 7
Next, we need to determine the length of the height. We know that the slope of the hypotenuse is 1.25, which means for every 1 unit moving in the x-direction, we move 1.25 units in the y-direction.
Since the base has a length of 7 units, to find the height, we multiply the length of the base by the slope of the hypotenuse:
Length_height = 7 * 1.25 = 8.75
So, the length of the height is 8.75 units.
Now, let's find the coordinates of the third point. The third point will have the same y-coordinate as the other two points since it lies on the same horizontal line.
Since the y-coordinate of the first two points is 2, the y-coordinate of the third point will also be 2.
Now, we can determine the x-coordinate of the third point. Since the third point lies on a line with a slope of 1.25, for every 1 unit moved in the x-direction, we move 1.25 units in the y-direction.
Starting from the first point (2, 2), we move 7 units in the x-direction to reach the third point:
x-coordinate of the third point = 2 + 7 = 9
Therefore, the coordinates of the third point are (9, 2), which completes the right triangle.