## Of course! I'd be happy to help you with these questions and guide you on how to find the answers. Here's a step-by-step explanation for each question:

1. Finding the midpoint of PQ:

- To find the midpoint of a line segment, we average the x-coordinates and y-coordinates of the endpoints.

- For point P(-7, 11) and Q(1, -4), the midpoint is calculated as follows:

Midpoint(x) = (x-coordinate of P + x-coordinate of Q) / 2

Midpoint(y) = (y-coordinate of P + y-coordinate of Q) / 2

Plug in the values and calculate the midpoint.

2. Finding the area of the rectangle:

- To find the area of a rectangle, we can use the formula: Area = length Ã— width.

- Given the vertices B(8, 0), T(2, -9), R(-1, -7), and C(5, 2), we can determine the length and width of the rectangle using the distance formula.

- The distance formula is: Distance = âˆš[(x2 - x1)^2 + (y2 - y1)^2].

- Calculate the distances between the given points to determine the length and width, then multiply them to find the area.

3. Finding the area of a triangle:

- To find the area of a triangle, we can use the formula: Area = 1/2 Ã— base Ã— height.

- Given the vertices (0, 0), E(3, 1), and F(-2, 6), we can calculate the lengths of the base and height using the distance formula.

- Once we have the lengths, we can plug them into the area formula to find the area of the triangle.

4. Finding the slopes of the diagonals of a rhombus:

- The diagonals of a rhombus are perpendicular bisectors of each other.

- To find the slopes of the diagonals, we can calculate the slopes of the lines connecting opposite vertices of the rhombus.

- Calculate the slopes using the formula: Slope = (change in y / change in x).

- The slope of one diagonal is the negative reciprocal of the slope of the other diagonal.

5. Finding the x-intercept of a line passing through two points:

- Given points (-2, -1) and (4, 3), the line intersects the x-axis when the y-coordinate is equal to zero.

- Set the y-coordinate of the equation of the line to zero and solve for the x-coordinate to find the x-intercept.

Remember, it's important to go through each step and understand the concepts involved in solving these questions. This way, you'll not only find the answers but also learn the process behind them. Good luck!