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 isosceles right triangles can she draw?

4  isosceles right triangles

Step-by-step explanation:

As 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 can be -2 or 5

7 is the distance between the y-coordinates of the third vertex and one of the given point

Either: 4 - y = 7 ⇒ y = 4 - 7 = -3

OR: y - 4 = 7 ⇒ y = 4 + 7 = 11

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

Therefore, the third vertex is (-2 , -3) , (-2 , 11) , (5 , -3) , (5 , 11)

 Amara can draw 4 isosceles right triangles

4  isosceles right triangles

Step-by-step explanation:

As 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 can be -2 or 5

7 is the distance between the y-coordinates of the third vertex and one of the given point

Either: 4 - y = 7 ⇒ y = 4 - 7 = -3

OR: y - 4 = 7 ⇒ y = 4 + 7 = 11

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

Therefore, the third vertex is (-2 , -3) , (-2 , 11) , (5 , -3) , (5 , 11)

 Amara can draw 4 isosceles right triangles

4

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)