The coordinates of two vertices of triangle DEF are D(-5,5) and E(9,8). Determine two possible coordinates for for F that would make DEF a right triangle ?
ans:
slope DE
= 8-5 / 9 - (-3)
= 3/12
I don't know this part :how to Determine two possible coordinates for for F that would make DEF a right triangle ?
just make DE the hypotenuse, and consider horizontal and vertical legs.
(-5,5),(9,5),(9,8)
or
(-5,5),(-5,8),(9,8)
Trying to make DE one of the legs makes things a lot harder.
To determine two possible coordinates for vertex F that would make triangle DEF a right triangle, we need to find the slope of the line perpendicular to DE.
The slope of DE is calculated as (8 - 5) / (9 - (-5)) = 3/14.
The slope of a line perpendicular to DE can be derived by taking the negative reciprocal of the slope of DE. In this case, the negative reciprocal is -14/3.
Now, we have the slope of the line perpendicular to DE, and we can use it to find two possible coordinates for vertex F.
To find the coordinates, we can start by assuming a value for one coordinate (either x or y) of point F, and then calculate the other coordinate using the slope formula.
For example, let's assume the x-coordinate of F is 0. We can use the point-slope form of a line to find the y-coordinate of F:
y - 8 = (-14/3)(x - 9)
Simplifying the equation gives us:
y - 8 = (-14/3)x + 42
y = (-14/3)x + 42 + 8
y = (-14/3)x + 50
So, one possible coordinate for F is (0, 50).
Now, let's assume the y-coordinate of F is 0. Using the same approach, we can find the x-coordinate of F:
0 - 8 = (-14/3)(x - 9)
Simplifying the equation gives us:
-8 = (-14/3)x + 126
(-14/3)x = -134
x = -134 * (3/14)
x = -29
So, another possible coordinate for F is (-29, 0).
Therefore, the two possible coordinates for F that would make triangle DEF a right triangle are (0, 50) and (-29, 0).