In the coordinate plane the vertices of rst are: r(6 -1), s (1 -4), t (-5,6). Prove that rst is a right triangle. State the coordinates of p such that quadrilateral rstp is a rectangle.

The triangle rst is a right triangle, and the coordinate of p such that rstp is a rectangle is (-10,3)

The coordinates of the triangle are given as:

Start by calculating the slopes of the sides of the triangle using:

So, we have:

Simplify

For the triangle to be a right triangle, then the product of the slopes must equal -1.

This is represented as:

So, we have:

Substitute values for rs and st

The above equation is true.

Hence, triangle rst is a right triangle

Calculate the distance rs using:

Calculate the distance tp using:

So, we have:

Opposite sides are equal.

So, we have:

Take square of both sides

By comparison, we have:

and

For

Take square root of both sides

Add 5 to both sides

So, we have:

Also, we have:

Take square root of both sides

Collect like terms

So, we have:

and

Hence, the coordinate of p is (-10,3)

Read more about coordinates at:

link

Coordinates of point p: (0,9)

Step-by-step explanation:

We have been given that in the coordinate plane the vertices of rst are: r (6, -1), s (1, -4), t (-5,6). We are asked to prove that rst is a right triangle.

First of all, we will find the slope between points 'r' and 's' and 's' and 't'.

We know that slope of perpendicular lines in negative reciprocal of each other.

Let us find the product of both slopes.

Since product of both slopes is , therefore, line 'rs' is perpendicular to line 'st' and 'rst' is a right triangle.

Let us assume that coordinates of point p are .

We need to find slope of point 'r' to 'p' is equal to slope of point 's' to point 't' and slope of point 'p' to 't' is equal to slope of point 'r' to point 's'.

Now, we have two equations and two unknown.  

  and  

To solve our system, we will use substitution method.

Upon substituting this value in equation (2), we will get:

Cross multiply:

Upon substituting in equation , we will get:

Therefore, the coordinates of point p at (0,9) that will make quadrilateral rstp is a rectangle.

1 and 2

step-by-step explanation:

its not b

step-by-step explanation: