Answer:
The possible first coordinates of point C are (-2.5,1.5)
The possible second coordinates of point C are (-9.5,1.5)
Step-by-step explanation:
we know that
Triangle ABC is a right isosceles triangle
so
Is a 45°-90°-45° triangle
AC=BC
we have
A(-6,-2), B(-6,5)
step 1
Find the length side of the hypotenuse AB
step 2
Applying the Pythagoras Theorem
Find the length side of leg AC
Remember that
AC=BC
substitute the given values
step 3
<em><u>Find the first possible coordinates of C</u></em>
The point C is located at right of point A
Determine the x-coordinate of point C
The x-coordinate of point C must be equal to the x-coordinate of point A plus the horizontal distance between point A and point C
Let
ACx ------> the horizontal distance between point A and point C
The horizontal distance between point A and point C is equal to the distance AC multiplied by cos(45)
we have
substitute
The x-coordinate of point C is
Cx=-6+3.5=-2.5
Determine the y-coordinate of point C
The y-coordinate of point C must be equal to the y-coordinate of point A plus the vertical distance between point A and point C
Let
ACy ------> the vertical distance between point A and point C
The vertical distance between point A and point C is equal to the distance AC multiplied by sin(45)
we have
substitute
The y-coordinate of point C is
Cy=-2+3.5=1.5
therefore
The possible first coordinates of point C are (-2.5,1.5)
step 4
<em><u>Find the second possible coordinate of C</u></em>
The point C is located at left of point A
Determine the x-coordinate of point C
The x-coordinate of point C must be equal to the x-coordinate of point A minus the horizontal distance between point A and point C
Let
ACx ------> the horizontal distance between point A and point C
The horizontal distance between point A and point C is equal to the distance AC multiplied by cos(45)
we have
substitute
The x-coordinate of point C is
Cx=-6-3.5=-9.5
Determine the y-coordinate of point C
The y-coordinate of point C must be equal to the y-coordinate of point A plus the vertical distance between point A and point C
Let
ACy ------> the vertical distance between point A and point C
The vertical distance between point A and point C is equal to the distance AC multiplied by sin(45)
we have
substitute
The y-coordinate of point C is
Cy=-2+3.5=1.5
therefore
The possible second coordinates of point C are (-9.5,1.5)
see the attached figure to better understand the problem