Answer:
The coordinates of point Y are (-4 , 1) OR (6 , 1) OR (-4 , 5) OR (6 , 5)
Explanation:
* Lets explain how to solve the problem
- Δ XYZ with vertices X = (1 , 5) and Z = (1 , 1)
- The area of the triangle XYZ is 10 unites²
- We need to find the third vertex y
∵ Point X is (1 , 5) and Point Z is (1 , 1)
- Points X and Z have the same x-coordinate
∵ The side XZ is a vertical side
- The length of any vertical segment is the difference between
the y-coordinates of its endpoints
∵ The y-coordinates of point X and Z are 5 and 1
∴ The length of XZ = 5 - 1 = 4 units
∵ The area of any triangle = 1/2 × base × height
∵ XZ is a vertical side
∴ XZ is the height of the Δ XYZ
∵ The area of the triangle is 10 unites²
- Substitute these value in the rule of the area
∴ 10 = 1/2 × base × 4 ⇒ 1/2 × 4 = 2
∴ 10 = 2 base
- Divide both sides by 2
∴ base = 5 units
∵ The base is ZY or XY and both of them are horizontal segments
∴ ZY = 5 units OR XY = 5 units
- The length of any horizontal segment is the difference between
the x-coordinates of its endpoints
# If the side is ZY
∵ The y-coordinates of the endpoints of the horizontal segment are
equal
∵ point Z is (1 , 1)
∴ The y-coordinate of Y is 1
∵ The length of ZY = 5 units
- The length of any horizontal segment is the difference between
the x-coordinates of its endpoints
∴ 5 = x - 1 ⇒ OR ⇒ 5 = 1 - x
∴ x = 6 OR x = -4
∴ The x-coordinates of point Y are 6 or -4
∴ The coordinates of point Y are (6 , 1) or (-4 , 1)
# If the side is XY
∵ The y-coordinates of the endpoints of the horizontal segment are
equal
∵ point X is (1 , 5)
∴ The y-coordinate of Y is 5
∵ The length of XY = 5 units
- The length of any horizontal segment is the difference between
the x-coordinates of its endpoints
∴ 5 = x - 1 ⇒ OR ⇒ 5 = 1 - x
∴ x = 6 OR x = -4
∴ The x-coordinates of point Y are 6 or -4
∴ The coordinates of point Y are (6 , 5) or (-4 , 5)
* The coordinates of point Y are (-4 , 1) OR (6 , 1) OR (-4 , 5) OR (6 , 5)