Use the image to answer the question.
An illustration shows the first quadrant of a coordinate plane. The x-axis and the y-axis range from 0 to 15. Two right triangles are graphed on the plane. One triangle is formed by connecting points plotted at coordinates left parenthesis 5 comma 9 right parenthesis, left parenthesis 5 comma 3 right parenthesis, and left parenthesis 2 comma 3 right parenthesis. The sides of this triangle are formed by solid lines. The second triangle is formed by connecting points plotted at coordinates left parenthesis 12 comma 6 right parenthesis, left parenthesis 12 comma 2 right parenthesis, and left parenthesis 10 comma 2 right parenthesis. The sides of this triangle are formed by dotted lines.
What is the ratio of the area of the smaller triangle in relation to the area of the larger triangle?
(1 point)
To find the ratio of the areas of the two triangles, we need to first find the area of each triangle.
For the larger triangle, we can use the formula for the area of a triangle: 1/2 * base * height.
The coordinates of the points for the larger triangle are (12, 6), (12, 2), and (10, 2).
The base of the larger triangle is the distance between the points (12, 6) and (10, 2), which is 2 units.
The height of the larger triangle is the distance between the point (12, 6) and the line y = 2. To find this height, we can subtract the y-coordinate of the point (10, 2) from the y-coordinate of the point (12, 6). This gives us a height of 4 units.
So the area of the larger triangle is 1/2 * 2 * 4 = 4 square units.
Now, let's find the area of the smaller triangle.
The coordinates of the points for the smaller triangle are (5, 9), (5, 3), and (2, 3).
The base of the smaller triangle is the distance between the points (5, 9) and (2, 3), which is 3 units.
The height of the smaller triangle is the distance between the point (5, 9) and the line y = 3. To find this height, we can subtract the y-coordinate of the point (2, 3) from the y-coordinate of the point (5, 9). This gives us a height of 6 units.
So the area of the smaller triangle is 1/2 * 3 * 6 = 9 square units.
To find the ratio of the areas, we can divide the area of the smaller triangle by the area of the larger triangle:
9 square units / 4 square units = 9/4.
Therefore, the ratio of the area of the smaller triangle to the area of the larger triangle is 9/4.