Question

Amara wants to draw isosceles right triangles on a coordinate plane that have two vertices at (-2,4) and (5,4). If the coordinates of the third vertex are both integers, how many different isosceles right triangles can she draw?
Fill in the banks to explain your reasoning.
For the right triangle to be isosceles and have both coordinates of the third
vertex be integers, a side from one of the two given vertices to the third vertex
must have a length of _____ units and be parallel to the ___-axis.
The y-coordinate for the third vertex must be _____ or _____.

Amara can draw ____ isosceles right triangle(s).

Answer 1

Answer:

The side must have a length of 7 units

and be parallel to the y-axis

The y-coordinate for the third vertex must be -3 or 11

He can draw 4 isosceles right triangles

Step-by-step explanation:

∵ The side joining (-2 , 4) and (5 , 4) is horizontal (same y-coordinates)

∴ Its length = 5 - 2 = 7

∴ The side from the one of the two given vertices to the third

   vertex must be vertical so it's parallel to the y-axis

∴ The x-coordinate will be -2 or 5

∵ The distance between the y-coordinates of the third vertex

   and one of the given point is 7

∴ 4 - y = 7 ⇒ y = 4 - 7 = -3

∴ y - 4 = 7 ⇒ y = 4 + 7 = 11

∴ The y-coordinate of the third vertex must be -3 or 11

∴ The third vertex is (-2 , -3) , (-2 , 11) , (5 , -3) , (5 , 11)

∴ Amara can draw 4 isosceles right triangles