Geometry Exercise 7.1

Study Notes

Distance Calculations

Distance between points (2, 3) and (4, 1) can be calculated using the distance formula: (d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}).
For points (-5, 7) and (-1, 3), apply the same distance formula to find the result.
For general points (a, b) and (-a, -b), the formula leads to a consistent relation regardless of specific values.

Specific Distance Example

The distance between (0, 0) and (36, 15) can be determined using the distance formula, yielding a specific numerical result.
This distance can then be compared to the distance between two towns A and B, analyzing if known values apply.

Collinearity Analysis

Determining if points (1, 5), (2, 3), and (-2, -11) are collinear requires checking if the slopes between any two pairs of points are equal.

Triangle Type Check

To verify if points (5, -2), (6, 4), and (7, -2) form an isosceles triangle, calculate the distances between each pair and assess if at least two distances are equal.

Quadrilateral Shape Confirmation

Assess points A, B, C, and D for whether they form a square by checking the distances between adjacent points and the diagonals.
Evaluation of points (-1, -2), (1, 0), (-1, 2), and (-3, 0) to determine if they form a specific quadrilateral, justifying the claims with distance measures.
Repeat for points (-3, 5), (3, 1), (0, 3), (-1, -4) and (4, 5), (7, 6), (4, 3), (1, 2) to classify the shape.

Equidistant Point on x-axis

Finding a point on the x-axis that maintains equal distance from (2, -5) and (-2, 9) involves setting up the equation using the distance formula, leading to a solution for the x-coordinate.

Distance Constraints

Establishing values of y that maintain a fixed distance of 10 units between points P(2, -3) and Q(10, y) requires solving the related distance equation for y.

Description

Test your understanding of distance, collinearity, and triangle properties in this Geometry Exercise 7.1 quiz. You'll solve problems involving distances between points, checking for collinearity, and determining the type of triangle formed by given vertices.