Two vertices of a right angle have coordinates (3,7) and (3,10). the segment that connects these points a leg of the triangle. which set of coordinates for the third vertex would create a right triangle?

(x,7) or (x,10)

Step-by-step explanation:

It is given that two vertices of a right triangle have coordinates (3, 7) and (3, 10), we can see that the x-coordinate is same for both vertices, therefore it is a vertical line and thus base of the right angle triangle.

We need to find the height of this triangle which will be perpendicular to this line, so the value of y-coordinate of third point must be either 7 or 10.

Example

(8,7)

13

step-by-step explanation:

distance formula is d=√(x2-x1)^2   +   (y2-y1)^2

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1