Triangle PQR is dilated by a scale factor of 1.5 to form triangle P′Q′R′. This triangle is then dilated by a scale factor of 2 to form triangle P″Q″R″. If vertex P is at (3, -4) and vertex Q is at (5, -1), what are the coordinates of vertices P″ and Q″?
To find the coordinates of P′, we multiply the x and y coordinates of P by the scale factor 1.5:
x coordinate of P′ = 3 * 1.5 = 4.5
y coordinate of P′ = -4 * 1.5 = -6
Similarly, the coordinates of Q′ are found by multiplying the x and y coordinates of Q by 1.5:
x coordinate of Q′ = 5 * 1.5 = 7.5
y coordinate of Q′ = -1 * 1.5 = -1.5
Next, to find the coordinates of P″, we multiply the x and y coordinates of P′ by the scale factor 2:
x coordinate of P″ = 4.5 * 2 = 9
y coordinate of P″ = -6 * 2 = -12
Similarly, the coordinates of Q″ are found by multiplying the x and y coordinates of Q′ by 2:
x coordinate of Q″ = 7.5 * 2 = 15
y coordinate of Q″ = -1.5 * 2 = -3
Therefore, the coordinates of P″ are (9, -12) and the coordinates of Q″ are (15, -3).