Question

Donte ordered the plans shown to build a skateboard ramp. Each unit represents one foot. He wants to keep the same slope of the ramp and extend the base of the triangle three feet. How tall will the ramp be

Answer 1

3 feet

Explanation:

The slope of line shows the steepness of that line. It is the ratio of the change in vertical distance to the change in horizontal distance.

The slope of a line passing through points
`(x_1,y_1)\ and\ (x_2,y_2)` on the coordinate plane is:

`slope=(change\ in\ y)/(change\ in\ x)=(y_2-y_1)/(x_2-x_1)`

From the diagram of the ramp, we can see that:

The ramp passes through the point (0,0) and (6, 2). Therefore the slope is:

`slope=(2-0)/(6-0)=(1)/(3)`

The base is at 6 ft tall, if we extend the base by 3 units, the base would be 9 ft (6 + 3). The new height would be:

height = slope * base = (1/3) * 9 = 3 feet

If the base is extended by 3 feet, the tall would be 3 feet tall.