Question

Triangle QRS is similar to triangle TUV. Write the equation, in slope-intercept form, of the side of triangle QRS that is parallel to segment UV. You must show all work to receive credit. Triangles QRS and TUV are shown. Q is at negative 2, 1. R is at negative 2, 7. S is at negative 8, 1. T is at 4, 2. U is at 4, 5. V is at 1, 2.

A. y = -2x + 5
B. y = 2x - 1
C. y = -0.5x + 3
D. y = 0.5x - 1

Answer 1

To write the equation of the side of triangle QRS that is parallel to segment UV, calculate the slope of UV and use it with a point from QRS to find the line's equation. The equation is y = -x + 3.

Step-by-step explanation:

To find the equation of a line in slope-intercept form (y = mx + b), you need both the slope (m) and the y-intercept (b) of the line. Since triangle QRS is similar to triangle TUV, and we are looking for the side of triangle QRS that is parallel to segment UV, we need to calculate the slope of segment UV first.

For segment UV, we have the points U (4, 5) and V (1, 2). To find the slope (m) of UV, we use the formula m = (y2 - y1) / (x2 - x1), which gives us m = (2 - 5) / (1 - 4) = 3 / -3 = -1. Therefore, the line parallel to UV must also have a slope of -1.

The point Q (-2, 1) lies on the parallel line in triangle QRS, so we can use the slope and this point to find the y-intercept (b).

Using the point-slope form (y - y1 = m(x - x1)), we get y - 1 = -1(x - (-2)), which simplifies to y = -x + 1 + 2, hence y = -x + 3. Therefore, the equation of the side of triangle QRS parallel to UV is y = -x + 3.