6 Consider the points P(4,7),Q(8,4),R(7,0), and S(-1,t). Find t given that PQ||SR.

Calculate Slope of PQ: Given points P(4,7), Q(8,4), R(7,0), and S(-1,t), we need to find the value of t such that PQ is parallel to SR. For two lines to be parallel, their slopes must be equal. Let's first calculate the slope of PQ. The slope of a line passing through points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). Slope of PQ = (4 - 7) / (8 - 4) Slope of PQ = (-3) / (4) Slope of PQ = -3/4Calculate Slope of SR: Now, let's calculate the slope of SR using the coordinates of R(7,0) and S(-1,t). Slope of SR = (t - 0) / (-1 - 7) Slope of SR = t / (-8) Slope of SR = -t/8Set Equal Slopes: For PQ to be parallel to SR, their slopes must be equal. Therefore, we set the slope of PQ equal to the slope of SR. -3/4 = -t/8Solve for t: Now, we solve for t by cross-multiplying. -3 * 8 = -t * 4 -24 = -4tDivide both sides by -4 to isolate t. t = (-24) / (-4) t = 6

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Math Problems

Algebra 2

Evaluate expression when a complex numbers and a variable term is given

Full solution

6

Consider the points

\mathrm{P}(4,7), \mathrm{Q}(8,4), \mathrm{R}(7,0)

, and

\mathrm{S}(-1, t)

. Find

t

given that

\mathrm{PQ} \| \mathrm{SR}

Calculate Slope of PQ: Given points $P(4,7)$ , $Q(8,4)$ , $R(7,0)$ , and $S(-1,t)$ , we need to find the value of $t$ such that $PQ$ is parallel to $SR$ . For two lines to be parallel, their slopes must be equal. Let's first calculate the slope of $PQ$ . The slope of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $Q(8,4)$ $0$ . Slope of $PQ$ = $Q(8,4)$ $2$ Slope of $PQ$ = $Q(8,4)$ $4$ Slope of $PQ$ = $Q(8,4)$ $6$
Calculate Slope of SR: Now, let's calculate the slope of SR using the coordinates of R $(7,0)$ and S $(-1,t)$ . $\text{Slope of SR} = \frac{t - 0}{-1 - 7}$ $\text{Slope of SR} = \frac{t}{-8}$ $\text{Slope of SR} = -\frac{t}{8}$
Set Equal Slopes: For $PQ$ to be parallel to $SR$ , their slopes must be equal. Therefore, we set the slope of $PQ$ equal to the slope of $SR$ . $\newline$ $-\frac{3}{4} = -\frac{t}{8}$
Solve for t: Now, we solve for t by cross-multiplying. $\newline$ $-3 \times 8 = -t \times 4$ $\newline$ $-24 = -4t$
Solve for t: Now, we solve for t by cross-multiplying. $\newline$ $-3 \times 8 = -t \times 4$ $\newline$ $-24 = -4t$ Divide both sides by $-4$ to isolate t. $\newline$ $t = (-24) / (-4)$ $\newline$ $t = 6$