Geometry Trivia Questions Test! Basic Quiz

Explanation
The equation of the line is 5x - 2y = 10. To find the x-intercept, we set y = 0 and solve for x: 5x - 2(0) = 10, which gives x = 2. Therefore, the x-intercept is 2. To find the y-intercept, we set x = 0 and solve for y: 5(0) - 2y = 10, which gives y = -5. Therefore, the y-intercept is -5. The gradient of the line is found by rearranging the equation to slope-intercept form (y = mx + b), where m is the gradient. In this case, we have -2y = -5x + 10, so y = (5/2)x - 5/2. Therefore, the gradient is 5/2.

Explanation
The equation of a line can be written in the form y = mx + b, where m represents the gradient and b represents the y-intercept. In this case, the gradient is given as -3 and the y-intercept is given as 4. Therefore, the equation of the line can be written as y = -3x + 4.

Explanation
The distance between two points in a coordinate plane can be found using the distance formula: √((x2-x1)^2 + (y2-y1)^2). In this case, the x-coordinates are -4 and -1, and the y-coordinates are 7 and 3. Plugging these values into the distance formula, we get √((-1-(-4))^2 + (3-7)^2) = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5. Therefore, the distance between P(-4,7) and Q(-1,3) is 5 units.

Explanation
In this question, we have a circle with a radius of 13cm and a chord AB that is 12cm away from the center. The length of the ladder can be determined by using the Pythagorean theorem. The distance from the center of the circle to the midpoint of the chord is the height of a right-angled triangle, and the distance from the midpoint of the chord to one end of the chord is the base of the triangle. By applying the Pythagorean theorem, we can find that the length of the ladder is 10cm.

Explanation
A polygon with six sides is called a hexagon.