Geometry Trivia Questions Test! Basic Quiz

1) Katie keeps her earrings in a beautiful glass case which has six sides. What is the name of a polygon with six sides?

Octagon

Hexagon

Nonagon

Quadrilateral

A polygon with six sides is called a hexagon.

Explanation

A polygon with six sides is called a hexagon.

2) The radius of a circle is 13cm and AB is a chord that is at a distance of 12cm from the center. The length of the ladder is:

35 cm

17.5 cm

25 cm

10 cm

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

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.

3) Find the axis intercepts and gradient of the like with the equation 5x-2y=10.

X-intercept = 4, y-intercept = -4 and gradient - 6/9

X-intercept = 4, y-intercept = -32 and gradient - 64/1

X-intercept = 4, y-intercept = -8 and gradient - 6/9

X-intercept=2, y intercept= -5 and gradient = 5/2

X-intercept = 1, y-intercept = -8 and gradient - 62/3

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 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.

4) Determine the equations of the following lines:
a) gradient -3, y-intercept 4 b)through the points(-3,4) and (3,1).

Y=3x+9

Y= -3x+4

Y= x+2

Y= -7-6x

Y=5x+4

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 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.

5) Find the distance between P(-4,7) and Q(-1,3).

5 units

8units

15units

12 units

10units

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

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.